I have used mostly TMY-2 in 120 and 35mm (a few hundred rolls) and a little bit of 4x5 (maybe 50 sheets), and very little TXP in 120 and 4x5 (maybe 10 rolls and 50 sheets).
My appreciation of the two films is as follows:
1. TMY-2 has grain that is far finer than TXP.
2. TMY-2 sees color differently. It is as though the UV blocker combined with an altered blue and red sensitivity makes for darker skies without a filter.
3. TXP has a longer toe, which essentially means that more of the shadow details will get buried in base fog once the film has been developed than with TMY-2, and it does so gradually (TMY-2 has an abrupt and short toe). As Drew points out, TMY-2 has the ability to reveal shadow detail VERY deep into the shadows, and that is because its curve shape (or tonality response) is flatter. Once you hit the toe on TMY-2, though, the details are gone, because it is very steep.
4. TMY-2 records a much longer brightness range than TXP, which means it is much more tolerant, or forgiving, of exposure extremes than TXP.
5. TMY-2 is more sensitive to development alterations, which means that it needs more control in terms of developer temperature, developing time, agitation, and such. It simply reacts faster to changes. That makes TXP more forgiving of developing errors.
6. TMY-2 can be shot at box speed and maintain great shadow detail. My experience is that TXP can not.
7. If you shoot TMY-2 at about EI 1,000 to 1,250, and then process the film in something like Xtol 1+1, you can get tonality that is confusingly similar to TXP. This is true of TMX also, if you shoot it at about EI 250-320 and process appropriately. I've done this comparison, and while grain and color rendition remains dissimilar, the tonality can be very similar indeed.
With all that said, I have stopped worrying about differences between films. Like Eddie, Michael, Mark, and others have said, the final output is infinitely more variable with exposure and developing technique than the intrinsic differences between different films. Among TXP, HP5, and TMY-2 none of those films are going to make my pictures any better. Right now I have a film stash that is way too mixed for my liking, but I can't say no to free film, so I have Tri-X 400, HP5, and TMY-2 in 120 rolls, and after I shoot with either of them, process, and make prints, the final print quality from either is so good that I basically don't care which is which. I only wish I could become a better photographer, and a better printer; I know that my materials will always be able to match and exceed my skill, and give me what I need.
I must say that ever since I came to that realization my photography life has been a lot simpler and more enjoyable. But to each their own, whatever makes you happy. Have fun!