Which one is better.

Which Weapon is better Leviathen Blade UV very high damage to CTR or Divine Avenger UV very high damage to CTR and why?
And how much are they worth?

not sure if you can deal damage to CTR....
really depends on preference, pretty sure the DA Very High CTR would be 'worth' more.
Good luck finding either of those for less than 20K CE.
CTR is a useless UV, since normal attacks do more damage. For a Leviathan it's best to find a UV for attack speed, as for divine avenger, some construct damage UV or CTR would be nice.
Although attack speed and construct UV's seem to be the most useful to Da's

The reason I ask is because I have a DA UV very high CTR. And
I have a friend with a Levi UV very high dam. CTR he ask me
To trade him .. so I just wanted to do some research.
You can't usually trade 5* equipment unless it was created prior to the 5/17 patch and also never bond to your character.
But I think you have your UV terminology a bit mixed up...
There is a UV CTR which stands for Charge Time Reduction. Then there is a different damage UV such as "Damage vs Slime: Very High". Also note that UVs are different from inherent abilities of a weapon as UVs are a bonus. All swords receive CTR Low at Level 5 and then CTR Medium at Level 10 - but these are separate from any UV.
Both kinds of UVs are very popular and highly sought after.

Oh. I was Thinking CTR was the acronym for construst.
Thank you for the correction.
Ah that makes much more sense now. I would say that a DA Damage vs Construct Very High is more useful than the same UV on a Levi for two reasons:
1) DA is elemental so already has a bonus to Constructs. The UV damage bonus would amplify this effect.
2) The third room of some arenas spawn a ton of bots and the DA's charge attack is preferable to the Levi's in that kind of situation. This is because the DA would keep the bots in a neat pack while the Levi would likely spread them. (This reason is subjective.)
On the other hand, the Levi has a nice charge attack for Gun Puppies. I'd stick with DA, however.
CTR is a community acronym. It won't say "CTR" anywhere on a weapon- it would list it as UV: Charge Time Reduction - Very High. So if you had a Divine Avenger with a UV Very High CTR, wouldn't you have known it was for Charge Time Reduction in the first place?

Like I said before.. I thought CTR was the acronym for Constructs.
I can't say too much, but it depends highly upon what weapon you would use. I think both are pretty highly valued, and would sell for at least a million crowns, probably two, each on the auction house. I think I just saw a DA with no UV go fro 1.25, although being a third party just seeing it it is hard to say.
Personally, I would use the Divine Avenger, since I use one anyways, and that charge attack is great to shove everything to the other side of the room, as opposed to just knocking them away from me.