Hay guise! I noticed there's been quite a bit of discussion about this a short while back so I decided to write a document on the matter. The reason I'm doing this is because people aren't really considering everything that there is to know before deciding what to get. Therefore, I present to you:
this.
For quick redirects, the URL http://tinyurl.com/LeviVsCIV also exists.

What? You don't want Google Docs? But it has a much better format! Oh well, here she is:

Introduction
Hey you Spiral Knight! I’ve noticed there’s been a lot of arguing about Cold Iron Vanquisher vs Leviathan Blade on the forums and I’ve recently found my love for Alice in Chains while already having had a Lionheart Honour Blade for a while. I am by no means an expert on the subject but I find that there are several things I’ve understood that others don’t consider at all.

If you’re new to the game, I suggest you hop over to the Abbreviations and such section by clicking the clicky in the Table of contents below before you start reading. Then we can talk.

Table of contents (clickies to come)

• Introduction
• Facts
• Stats
• Other facts
• In Fihurrdurrstorm Citadel
• Who should use which blade?
• Summary
• TL;DR (summary of the summary)
• Abbreviations and such
• Sources
• Todo
• Changelog
• Contact

Facts
Oh well, first things first. Let’s look at the facts we know and have confirmed.

Stats
These are the stats of the swords*
Note: these stat images are incorrect. I will correct them as soon as I have fully heated my Cold Iron Vanquisher.
Okay, so what we have here is Leviathan Blade’s and Cold Iron Vanquisher’s stats, retrieved from wiki.spiralknights.com 20/01-2013. It should be noted that CIV has a damage bonus against the Undead that is High, i.e. 3. First, we have Levi’s stats, followed by CIV’s. The third part is a comparison of the damage bars. What we see here is actually quite weird. Leviathan Blade has seven more pixels on the bright blue bar while CIV has two more on the dark blue bar. What is this madness? After all, it is a known fact that CIV is weaker than Levi! Besides, we can’t get any real damage numbers out of this. Let’s have a look at the real numbers, then!
*In the comparison, CIV is the top bar.

The following list lists damage versus enemies at Depth 24 using both swords with no damage bonuses (apart from the one CIV has against Undead that is High). Data from Spiral Knights Wiki (Leviathan Blade and Cold Iron Vanquisher)

Leviathan Blade
• Strike 1 & 2 dmg: 193
• Strike 3 dmg: 241
• Charge attack dmg: 355

Cold Iron Vanquisher
• Strike 1 & 2 dmg: 177
• Strike 3 dmg: 223
• Charge attack dmg: 330

Cold Iron Vanquisher vs Undead
• Strike 1 & 2 dmg: 213
• Strike 3 dmg: 265
• Charge attack dmg: 385

Okay, let’s see if there’s any sensible maths behind this! Let’s start with simple addition and subtraction.

193 - 177 = 15
241 - 223 = 18
355 - 330 = 25

If there is anything we can see already, it’s that the damage difference gets bigger the higher the damage gets. Let’s apply percent on this!

193 / 177 = 1,090395480225989 ~= 109%
241 / 225 = 1,071111111111111 ~= 107%
355 / 330 = 1,075757575757576 ~= 108%

Oh dear. These numbers would be hard to make any sense out of. Don’t ask a kid to do it, at least. No matter, we can make out the fact that Leviathan blade is about 8% stronger than CIV. Let’s crunch more numbers!

213 / 193 = 1,103626943005181 ~= 110%
265 / 241 = 1,099585062240664 ~= 110%
385 / 355 = 1,084507042253521 ~= 109%

We can conclude that CIV is roughly 10% more powerful than Levi against the undead.

213 / 177 = 1,203389830508475 ~= 120%
265 / 223 = 1,188340807174888 ~= 119%
385 / 330 = 1,166666666666667 ~= 117%

And now we know that the Undead bonus on CIV increases the damage against them by roughly
19%.

I think that’s enough maths for this document. If we are to round these numbers, Levi is about 10% more powerful than CIV except against the undead, where CIV deals 10% more than Levi.

The two blades are identical in attack speed and range, if you did not know.

Other facts
You will now be enlightened as I shall tell you about one of the greatest things about CIV:
It has less knockback than Levi. This means that CIV is much more party friendly and will not send slimes in your friends’ faces, at least not as often.

CIV is more likely to multihit with the charge on mobile smaller enemies due to the extended time that the enemy remains within range.*
*Untested by myself, source: BSG.

Yet another thing about CIV’s lowered knockback is that it’s more efficient with Vortex line bombs because it won’t send the enemies around Cradle twenty times before they land. This is actually untested but I have tested Levi with Vortexes and I have found that it’s just a tad too powerful to keep the enemies constrained.

Keep in mind that lowered knockback isn’t all good though. The extreme knockback that is Levi’s charge is a great defensive move, especially when one is going solo.

Oh, did I mention that CIV looks way better than Levi by the way?

In Fihurrdurrstorm Citadel
If you’re boring and in need of heat, cash, and/or energy all the time like everybody, chances are you’re going to spend a lot of time in FSC. Cool knights like Fehzor wouldn’t have to consider this part but chances are you're not Fehzor unless you are Fehzor, so let’s have a look at the ultra boring ruin that we all grind gear for so that we can grind more gear!

First, there’s the use of normal damage.
Every oiler encountered in the Citadel has a tendency to get lit by Shadowfire or Red Rovers. Piercing and Elemental aren’t effective against lit oilers and Shadow is pretty worthless in FSC, apart from the dozen Slimes or so. But what’d make one choose Normal over Shadow, then, you might ask. First of all, a Normal weapon would be useful against all enemies, while a Shadow weapon would only be useful against the Slimes. Do note that there are very few slimes and even fewer oilers in FSC, with no oilers after depth 25 (Charred Court), so this shouldn’t weigh too heavily although a normal weapon is still very desirable for reasons stated two paragraphs below.

Function in weapons is something that should never be overlooked. Levi is indeed more useful against the oilers but since over 90%* of all the enemies are Slag Walkers in FSC, CIV gets an edge against Levi there.
*Estimated.

The last and greatest pro of bringing a Normal weapon to FSC, however, is kicking Vanaduck’s mask’s butt*. Levi, DVS and Peppery Volcanobox are some of the greatest weapons for this. The reason, you might question, is that Vana’s mask is resistant to all damage types but Normal. Do note that Levi is more efficient than CIV towards the mask as the mask is not Undead.
*Vana’s mask does not have a butt.

Who should use which blade?
There’s no question about me preferring CIV over Levi, but I wish not to angle this all too much. If you’re looking for a primary damage source, choose Levi. But do consider the fact that other specialised weapons are stronger. If you’re looking to kill Vanaduck as fast as possible, do note that Dread Venom Striker has higher DPS than Levi* and Levi therefore suboptimal for Vanaduck’s mask, although it is indeed more effective than CIV. Even more effective is probably Volcanic Pepperbox, especially if one goes for max gun stats for Blitzes.
*Source: Lancer Knightz Depth 24 Sword Damage data. It should be noted that DVS’s poison bring the damage even higher although it’s very important to note that Levi has a devastating charge against the Mask as it will always be hit thrice since it doesn’t afraid of anything, including knockback.

Another reason to roll with Leviathan is that CIV’s advantage that is an Undead High bonus comes in the form of - I already said it - a damage bonus. This means that CIV can be made almost completely worthless in comparison to Levi if one goes for higher than High damage bonus through armours and trinkets. Therefore, I do not really recommend CIV to swordies. But of course, there’s still the reduced knockback that weighs quite heavy in my opinion. Any party-player should really consider this, too.

Damage bonuses isn’t the only reason to skip CIV, however, as most swordies find themselves - and should find themselves - wielding an elemental sword when there are Undead or Constructs about.

You might’ve noticed how much empathy I’ve put on FSC. That is because I’m a veteran player with almost 900 hours behind my character and I can safely say how much time you spend there. A LOT. Additionally, two out of four Danger Missions include Undead monsters, one consisting of almost only Undead (LoA). It should also be noted that some upcoming content, potentially an expansion, will contain new Kat content and the last time I checked, Kats were pretty living yet dead. I can only link to this as anything else would require digging in the SK files and that would be posting spoilers and that’s not allowed. Please take all these statements about Kat kontent with a grain of pepper as we can’t really know anything except that Nick is making Kat gear.

Summary

• Levi is stronger than CIV but CIV has a High (3) bonus against the Undead.
• If CIV deals 100 damage, Levi deals about 110 and CIV deals about 120 against Undead.
• The two are equally fast.
• The two have identical range.
• CIV has less knockback on the charge.
• This means CIV is more likely to multihit mobile smaller enemies with the charge.
• CIV won’t quite knock enemies out of Vortex line bombs with the charge.
• Levi’s charge is more defensive due to the greater knockback.
• CIV looks better, it’s a fact.
• Normal weapons are great side weapons in FSC.
• CIV generally wins over Levi in FSC, but...
• Levi is more effective than CIV against Vana’s mask since it is not Undead.
• DVS is roughly equal to or better than Levi for the mask anyway.
• Even better is probably Volcanic Pepperbox.
• If you’re looking for a primary damage source in CIV, you’re doing it very very wrong.
• CIV can be close-to-obsoleted by having more than High DI from armours and trinkets.
• CIV’s lowered knockback remains and means it’s better for parties.
• The final and most visited stratum, FSC, is inhabited by the Undead.
• So is Legion of Almire and Ghosts in the Machine.
• You will spend a lot of time in FSC. A LOT.
• There’s probably some new Kat content coming out!

TL;DR (summary of the summary)
If you’re a swordie, get Levi. But keep in mind that other weapons have better DPS. CIV has a lower knockback that is actually very useful, not to mention more party friendly. You’ll spend a lot of time in FSC, so that’s one good reason to get CIV.

CIV < Levi < CIV vs Undead.

Abbreviations and such
I’m using quite a few abbreviations and stuff in this guide/document/whatever. If you’re experienced, you probably know most of them. If not, common sense will help you come a long way. You should probably read through this article if you haven’t.
Back to the ones used in this duckument, here’s an unsorted list of them:

• Abbreviation: Full meaning (clickies)
• Levi: Leviathan Blade
• CIV: Cold Iron Vanquisher
• DVS: Dread Venom Striker
• DI: Damage Increase
• ASI: Attack Speed Increase
• CTR: Charge Time Reduction
• DPS: Damage per Second
• BSG (10/10, would read again): Bopp’s sword guide
• FSC: Firestorm Citadel
• LoA: Legion of Almire

Sources

• Experience
• Common sens
• The Spiral Knights wiki (http://wiki.spiralknights.com)
• Bopp’s sword guide (http://wiki.spiralknights.com/User:Jdavis/Swords)
• Lancer Knightz data (http://wiki.spiralknights.com/Lancer_Knightz_(Guild)/Data)
• All the cool people who posted in my thread (http://forums.spiralknights.com/en/node/73378)

Todo

• Correct stat images.
• Research what’s the most efficient versus Vanaduck’s mask.

Changelog

• ??/01-2013: Initial creation.
• 25/01-2013: Re-did some formatting
• 26/01-2013: Added Todo section, noted that stat images were outdated, reordered sections, noted and corrected according to Bopp’s criticism here and Fradow’s criticism here, removed some “very”s from the summary, added a source for Kat content,other minor changes.
• 26/01-2013

Contact
If you’ve got anything to say or ask me regarding this document, feel free to send a mail or whisper to Krakob in Spiral Knights. I’d love to help ya out if you can’t decide or add info if there’s anything that I’ve missed.

I’m one of ‘em Swedes so I won’t be on during late US hours. Therefore I suggest you mail in favour of PM, or send a friend request and /tell me something when I’m online to avoid mailing costs. You might also get the chance to contact me through the forums. I’m probably posting this in a thread on the forums.

Oh yeah, I run a small IRC channel that is #sk @ irc.Durd.net (clicky).
Come visit and idle with us! I go by the nickname Jakob there.