Its hard to define the Warhawk. It just is what it is, in many ways. Some mechs, like the Bain 3 or Hellstar, are just numbers mechs, the Warhawk is in many ways a feel mech.
One big upshot in any veriant is the 'fixed' TC (since TCs are veriable size, it can't really actualy be fixed under the rules as I understand them, so technicaly you can build a legal Warhawk with no TC, but its in the fluff, and no one who's sensable ever ignores it because TCs are awesome) and all the fixed sinks. It gives the Warhawk a cherictor as a long ranged mech, much like fixed JJs give mechs like the Summoner and Nova a bit of cherictor. Add to that the Warhawk tends to take advantage of that TC with ranged guns (the problematic B is a notable exception) and again, you start to get a feel for the mech as a whole that defies its omni nature. Some more modern omnis try to be all things, which on paper is the idea of an omni mech (the Periah is a good example, or the recently talked about Flamberge) but it makes it hard to talk about the mech as one thing or another. The Warhawk tends not to be like that. The Prime, A, C, D, all play very similarly, and the B, E and H are only about a half a step difrent. There's no real outlier veriant there.
Honestly the C is probably the most used, even if the Prime is the most known and talked about. No one really, when they're honest, wants to work that heat (I don't mind it, but only in fun games, not really competitive ones). The C largely solves that, and adds accuracy to the moon. The A gives up power and mixes the ranges up, but its a lot less BV and so wins for value, with the D being a nice evolution of it.
Thouse veriants are probably the mech's biggest up shot. A Dire Wolf with two PPCs, two LPLs and a TC would be almost too much to contemplate, and look how people speak about the Hellstar. But the Warhawk pulls it off just fine, thank you, and as a resualt its looked on as a match for thouse mechs, a legitimate alternitive to the very best assualt mechs, despite on paper looking like something of a runner up.