I've always found the grain structure of TMZ more appealing. I can't be the only one here, huh? (With TMZ I use x-tol 1:1 @3200 or 1600) My experiences are opposite of fhovie's in terms of tighter grain; I have found Delta more pronounced. Delta 3200 has a much flatter contrast as timeunit mentioned. And for skin tones seems a bit muddy to me. I've shot Tmz extensively and delta occasionally, but have developed by hand countless rolls of both for other photographers. I don't have a preference for any manufacturer...only the results I can get with their film. Ilford, Fuji, and Kodak all offer a high speed film that I would use for particular situations. Obviously, you should shoot a roll of both from your picks here and see what you prefer.
Your developer will make a big difference too.
The long answer and the only way to truly know for yourself is testing. Suggestion recap: TMZ and X-tol 1:1, EI 1600