...would probably make balancing a lot easier.
CC already has different values for PVP and PVE, some abilities (Colossus Smash) have different values as well, so why not damage?
Tooltips could be adaptable (you can activate if you want to see PVE, PVP or both) and balancing would give less headaches to the balancing team. If in example a class is perfect in PVE, but the damage in PVP is lacking, they just have to increase the PVP portion of some skills.
Another solution is to give damaging CDs or abilities PVP Power bonuses, like, "Increases the damage by 20% and PVP Power by 300". Or even add baseline PVP Power to auto-attacks for melee/hunters if required at any point.