Shards, pbox, toxic needle, BAB or ITD, bombs in general, cutters, winmillion, magnus lines, tortoguns.

I think the most unpopular weapon is actually CIV, because the absolute worst weapons are used for novelty. Literally the only thing CIV has going for it is looks.

You forgot that brandish does all of the things you listed for pepperbox, and Supernova is much harder to actually kill things with because of the massive knockback. Also:

Callahan: low damage, not mobile, no knockback

Slug: Worse in every way than Cally, including no stun

I've got Furious Flamberge. It's fun to use sword, because fire happens often while charging. But I need to use BTB in the same time, because normal damage sucks.
Shard Bomb are not that bad. True bomber always will have one. Though old ones were just better.
Winmilion's only fault is that theres no 5* version of it. It's really fun to use this sword.
Pepperbox, well all I have to say is: Gunner update.
Cutters are OK with asi when fighting on not dangerous missions, but pretty useless in anything else.
Catalyzers also: Gunner Update.
CIV has just no hope, but it looks nice. xd
Supernova is OK enough, because it's knockback + damage for every monster family. This one actually should be more popular.
Callahan and Slug: Gunner update.

What is CIV

Unpopular? Proto sword

I saw proto bombs used in tier 3 compounds (some challenge thing)

The guys amazingly poo

@Klipik

Pepperbox has two advantages over the brandishes- normal damage (which makes it one of my favorite guns against wolvers) and a long range normal shot that deals moderate crowd control via lighting random things on fire. This makes it play differently than a brandish would, and while the brandishes might play faster and have the upper hand in many situations, pepperbox can still stand on its own and exist as a perfectly fine choice of weapon.

@Things I forgot

Thanks for the ones I forgot, I just kind of wrote that without looking stuff up quickly...

Callahan/Slug = crap mobility + mediocre damage, but more than that complete reliance on flinch mechanics that are liable to fail.

Rigadoon = Actually decent, as it deals stun which many piercing-weak monsters are weak to. Good when you don't need the damage.

Flamberg = In line with cold iron vanquisher

Plague Needle = Mostly just a downgrade from blitz needle. Is better against crowds w/ healers in theory, but rarely have I seen a spot for it.

The grill is a reskin of the pure elemental shard bomb.

Said shard bomb is an OK weapon. It isn't particularly "good" for much, and is basically a worse time investment than would be the "mainstream bombs", dark retribution + dark briar barrage.

Basically:

Undead:

Kats = hard to bomb w/ shards, but shards are actually better. Guns + swords are still nicer in general.
Zombros and the citadel = Dark briar barrage works well against these, and does no knockback.
Legion of Almire crowd = Bombs in general aren't good against the hardest parts of this.

Construct:

Turrets = dark retribution is WAY more effective, regardless of damage types
Retrodes = Crystal bomb knocks them and their lazors about randomly. Dark retribution is safer.
Lumbers = small amounts of knockback are scary; dark rets allows damage at a distance.
And so on.

An elemental dark retribution would be SWELL for bombers.

I would agree with Holy-Knightmare on the Katnip Pouches, but they aren't weapons

Well yeah but the brandishes are boring swords that are perfect because of how vanilla, boring, easy to master, and powerful they are. They make you strong early on and keep you that way, but leave you wanting for more, and with good reason- other weapons are more interesting and powerful when used correctly. Dark retribution is the same way, or would be if it were standardized in some way and given more options for good damage output.

What about the most unpopular armor and shields? (Tier 3, that is)

I suppose I'm not apart of that demographic then, as usual.

Funny thing, I only have one brandish and it is the Apocrean one, rather uncommon not just due to it's difficulty of obtaining but the fact that it isn't as powerful as Acheron. Honestly a 4star Silent Nightblade is almost as powerful as the Obsidian edge.

The Fang of Vog description scares away most people and those that do get one are often turned off by it's slow swing speed.

@ PandaFishie

What Zeddy said but I would leave out demo suits since most just stick with Chaos for bombing.

PvE gunner here - The pepperbox isn't too useful right now, but in the gunner update beta it has been buffed significantly - it may be very useful after the fabled update arrives, so don't sell yours off yet! Plague needle on the other hand, not so much.

Cala and slug are useless now, and remain useless in the gunner update beta - they're just too slow and don't deal enough damage to be practical.

The catalyzer line may be unpopular, but the biohazard is certainly viable in general PvE. The neutralizer, not so much - the supernova does its job better. In anything except beast compounds, the polaris is the better choice anyways. Using a bio + umbra driver swap setup deals slightly more dps than alch swapping between two umbras, and comes with the advantage of having the bio's poison and crowd clearing/positioning charge attack, but at the expense of having a higher skill floor due to the nature of catalyzer charge attacks.