Theory-crafting: What is better? A PVP power gem or an agility gem for PVP? Which gem should you use if you are a jewel-crafter? 320 Agility or 320 PVP power? PVP power rare gems give 320 PVP power. Agility rare gems give only 240 Agility. There are Jewel-crafter only gems that give 320 agility but there are no jewel-crafter only gems for PVP power or resilience.
I used my rogue to make these calculations. Level 87 with these stats: Main hand DPS 4225. I did not include the offhand DPS to keep things simpler.
According to my character stats: 1 agility -->2 attack power-->0.143 DPS
Plus 0.00175% increase in crit chance. Each crit is about 1.5 times my total DPS. So 1 agility also increases my total DPS by 0.00175% x 1.5 = 0.0026% increase in my total DPS.
A jewel-crafting only gem that gives 320 agility for my level 87 rogue:
320 x 0.143 DPS = 45.76 DPS added to my total DPS of 4225 = 4270.76 DPS for my main hand. The additional DPS from the added crit is: 320 times 0.0026% = 0.832 % in DPS. 0.832% x 4270.76 = 35.5 DPS.
320 Agility for my level 87 rogue therefore increases my main-hand DPS from 4225 to 4306. But we are not yet done. Players have 40% reduction in damage from other players at baseline because of resilience and they can of course increase this resilience with gear, enchants and gems. (1 – Opponent’s resilience) x my DPS is the damage I will be doing.
In my rogue’s case against a PVE player: (1-.4) = 0.6 x 4225 = 2535 DPS without my agility gem and 2584 DPS with the 320 agility gem (1.93% increase in DPS).
If my opponent was PVP geared with say an extra 20% resilience then these are the calculations: (1-.6) x DPS and the results are: 1690 with no gem, and 1722 with the gem (1.89% increase in DPS).
A key point here: stacking resilience reduces your enemy’s damage output exponentially as you approach 100%. PVP power can counter that. I have another comment on this topic elsewhere, but this leads me into the discussion of the PVP power gem.
On my level 87 rogue, each PVP power point reduces my opponent’s resilience by 0.0078%. For a rare gem 320 X 0.0078% = 2.5% reduction in resilience and results in these changes in DPS:
My baseline DPS is 4225 but against a PVE player with no extra resilience the DPS is 2535 (see above). With this gem his resilience is down to 37.5%. (1-0.375) x 4225 = 2641 (4.2% increase in DPS) which is 57 more DPS than with the 320 agility gem. So every point of DPS is superior to a point of agility on PVP.
...But consider what happens if the opponent has a lot of resilience and in this case an extra 20%.
Without the PVP power gem: DPS is 1690 (see above). With the gem my DPS is 1796 (6.3% increase in DPS). This is 74 more DPS than the agility gem. The more your opponent stacks resilience the more powerful PVP power becomes.

Summary:
In PVP, PVP power is far more potent than agility. Even a jewel-crafter only gem of agility will not compete with a rare (blue) PVP gem and I estimate that the PVP power gem is 2-4 times more potent depending on the resilience of your opponent.
Stacking resilience adds benefit exponentially with the more resilience you have.
The more your opponent stacks resilience the more powerful PVP power becomes. But it is still useful against players with no additional resilience because of the 40% baseline resilience that all players start with.

Numbers for my level 87 rogue:
Baseline main-hand DPS: 4225
No Gem-------------------------------------------------------------320 agility gem------------320 PVP Power gem
DPS against PVE player: 2535------------------------------------2584 DPS---------------2641 DPS
----------Extra DPS gained----------------------------------------------49----------------------106 (216% additional DPS)
DPS against player with 60% resilience: 1690----------------1722 DPS---------------1796 DPS
----------Extra DPS gained------------------------------------------------32------------------------106 (331% additional DPS)

Disclaimer: These calculations were made based on a level 87 combat rogue with specific gear. I have not calculated it for other levels or different gear and for other classes or specs. I have also not field tested it. You should do the same exercises for your character to see what advantages PVP power has over other stats such as strength or intellect.

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