IIRC, TMUA/MAT questions differs in style, but content-wise they're practically the same. Just try out the exam papers and you'll understand a bit. The only things that I remember appearing on TMUA but not MAT are those logic questions, which aren't too dfficult imo.
That said, if you feel like taking two entrance exams is a bit tough, Warwick mostly looks at STEP anyway. A bad score in TMUA (or none at all) doesn't mean an immediate rejection from them. I have no idea how good do you need in TMUA (or MAT in the past) to actually get a reduced offer - I doubt Warwick admissions even answers this question other than "it differs from year to year" (but worth a try if you really want to know).
The upshot here, though, is that it's better if you ask Warwick/Oxford admissions directly.