I think we should just rejoice in the fact that both versions of Tri-X as well as TMax 400 are available to us today. All of them are amazing films, each with some individual strengths. The day either of them become unavailable will be a sad day.
Having used both TX400 and TMY/TMY-2 a fair bit I have to say I often need to look at the negative itself to tell what film it was unless I remember. In using them I find Tri-X 400 is more forgiving in processing, in that it reacts to processing alterations slower, and TMY-2 is more forgiving in exposure in that it records a longer brightness range, but it reacts much quicker to processing changes, so it might be a little bit more difficult to handle in the darkroom. Tri-X has lower resolution and more grain, for better or worse (depending on what you want). But other than that I find that they are more similar than they are different and it's easy to use both films to make the type of negative that my paper likes, and to me when I get the print just right, the rest becomes academic and no longer even interests me.