PvP in this game wasn't really even a consideration when they though of in Final Fantasy XIV it seems. When it was released, there wasn't any kind of PvP, and was added in a later patch.
When they first added it, it was pretty popular and you'd find a queue pretty quick for it. The downside at the beginning though was the wait time from when you spawned in the area, to actually fighting was a full 60-seconds. Now, this may not seem like too much, but when the matches take less time then the waiting, it can get bothersome.
On top of that, the leveling for PvP was ridiculously slow. You needed to grind sooo much to get to where you can wear the high level PvP gear.
I stopped playing before Heavensword, so I am not sure how it is now, but when I quit it was pretty much the same. They did lower the waiting time once you get in, but no one really PvPs anymore and the ones who do just trade wins.
But overall, if you're looking for an MMO with a strong PvP element, Final Fantasy XIV would not be your game.