Tribes is only PvP, very fast paced and requires a LOT of practice to get good at considering that there are hardly any hit-scan (Meaning no travel time with your bullets. The moment you click, the bullet will hit) weapons and you gotta hit targets that are going at least over 200 Kph while expected to match that speed in a lot of cases.
Planetside 2 is also only PvP, and it's a game where you really can't solo. It's a 6000 player (2k per faction) 24/7 all out war. Think GW2's WvW but on a massive scale.
BF3, I can't comment on, but if it's anything like CoD, it's too different to compare to Firefall.
Firefall has PvE and PvP separated, no weapons are truly hit-scan, but some bullets go fast enough that you might as well consider it to be. It is more of a persistent world like in GW2, and it is class-based. You can change around your classes (aka: Battleframes) by buying new Battleframes and switching them.
It's not comparable to BF3, PS2, or Tribes. Beyond the fact that they're shooter's, they are just too different. I will say that Firefall is a very unique and great game, though it's still got a long way to go from a full release. I would totally recommend playing.
I have not logged into it in about 6 months but it never did grab me.
They did a massive gameplay overhaul since then. I suggest patching your game and trying it out.