(Submitted by Kongief)
T.Hawk is a very match-up knowledge oriented character. As with any other character, but I feel like with him it's a lot safer just to go into training and figure out what moves have higher priority than others because a lot of his moves,combos, and ways to get in leave you at a significant disadvantage on block.
Example: When I use Tomahawk Buster as an anti-air, at times I will get stuffed on jump-ins by a very random attack that I feel as though I should have some priority or frame advantage over. This is why I like Thrust Peak as an anti-air because if I whiff his DP I don't have enough recovery time to block where as the Thrust Peak, even if it whiffs it's such a fast attack that I'll have time to block most of the time. This is sort of a give and take move, you sacrifice the raw damage of a Tomahawk Buster as an anti-air but it's less risky so I only use the Tomahawk Buster when I'm positive that they're too far away for Thrust Peak to hit (down+forward jab).
if you have somebody cornered and do EX Tomahawk Buster and follow up with EX Condor Dive at the appropriate time, the Condor Dive will cross them up. You have to hit the EX Dive rather quickly, but you get the idea. The EX Condor Dive only comes out after the EX Tomahawk Buster has been blocked.