A tank's primary functions are to A) hold enmity and B) not die. Currently the PLD can hold hate well enough so that A) doesn't matter in most situations save AoE threat, and the number of situations where WAR's AoE threat capacity is going to make much of a difference is very limited. And a PLD is currently much better at B). DPS (as a tank) is a secondary function and is less important than the first two, which makes a WARs better DPS (in tank stance) a relatively minor bonus.
It's not about different playstyle, it's about math. Go check out the Tank forums and find one of the comparison threads that have an extensive breakdown of the 2 classes and the abilities they get (try to ignore all the "i feel" posts, most of that is garbage).
I'll not get into the specifics (they've been gone over in that forum enough) but the basics are that a PLD requires, due to shield oath + shield block + rage of halone + superior defensive cooldowns, a lot less healing to stay alive in any situation where there's a lot of incoming damage (any situation where anybody's going to care). And a WAR's self healing, no matter how many offensive stats you stack (offensive stats usually come at the cost of defensive stats, so it's not a straight bonus here), cannot close that gap. And thus people will much more often prefer a PLD because it's just a safer tanking option (especially when dealing with new or difficult content) no matter how much skill the WAR has.
And to further throw salt in the wound, there are a number of end game fights where PLD specific bonuses (no cooldown stun, a silence, ability to massively reduce incoming damage) are extremely desirable, while there are few if any fights that cater to the WAR (higher actual HP, not to be confused with effective HP, a healing debuff, better AoE threat, and maybe 10-15% extra optimal DPS in tank stance).