I tried stacking Alacrity, and there are some surprising benefits. Since it lowers your CDs, you get your special abilities faster (defensive cooldowns, leap, disruption, etc). Obviously your offensive abilities come more often as well. All things being equal, Alacrity is better because it both boosts your damage/second (by reducing the seconds) and causes your cooldowns to come around more often.
The problem with PvP is that all things are never equal. I found that you would frequently find yourself popping out of range and having to re-locate your target (or find a new one). Since you've invested all your eggs in the attack speed basket, any time spent not using abilities is "lost". By the time you find a target and get in range someone else who stacked power instead would have their abilities off cooldown, thus negating the benefit of your alacrity. The only difference at that point is that their attacks are more powerful.
For that reason, stacking alacrity is great for PvE but poor for PvP.