A question of weapons, PvE vs PvP

I have 4 ascended PvE characters which I love dearly and don't intend on deleting, and thus I have a question you people who commonly PvP with specific PvP characters can answer for me. I've got one of these PvE characters nearly to the point of having everything I could possibly want for PvP (nearly all skills, all secondaries, max weapons, etc.). Now, I was playing some PvP on her today, when I was told by a fellow that PvP weapons are better than PvE weapons and thus no one who's serious should play PvP with a PvE character.

My question is this: why are PvP weapons better? Is it simply because they're max damage and (probably, if you've unlocked them) have max mods while PvE weapons with max damage and all max mods are harder to come by? Or is there something actually different about PvP weapons? Back before I had all of my four character slots used up I used to create PvP characters (and usually delete them shortly thereafter), and I don't recall anything that would make the PvP weapons somehow better than PvE ones.

Also, this brought up another question. Some of the collector weapons for casters in PvE are exceptionally good (I'm thinking the casting/recharge time 20/20) and I've got more of these than is probably healthy for any one individual. lol In any case, I don't remember such weapons as those when I was creating my PvP characters way back when. Are those 20/20 caster weapons available to a purely PvP character? Or are the best caster PvP weapons simply ones with max energy/damage and upgrades?

Once again, I'd check for myself by simply making a PvP character... except I'm out of slots and don't want to delete the PvE characters I've poured such an ungodly amount of time into.

PvP characters are equipped with 20/20 casting/recharge staffs for casters and +15% damage while in a stance/enchanted/hexed weapons for warriors. These types of weapons are generally available through PvE by dealing with collectors.

There is no difference between those collector weapons and thier PvP counterparts.

EXCEPT for the fact that some PvP weapons are not availible through collectors. For example, have you ever seen a +15>50 collector sword? Nope, only enchanted.