I've been a diehard Tri-X user since high school and I have to admit that TMY-2 is the first film that has been a serious contender to lure me away.
The grain is astonishingly small for a 400asa film. Basically it's as good as a traditional 100asa stock. Truly amazing.
Basically I have settled on Tri-X for bright sunny days. The shoulder roll off holds highlights forever and I still think it's one of the best looking film stocks around. There is something about the contrast of TMY-2 in bright sunlight that I don't like. I use Barry Thornton's 2-bath to keep the contrast under control.
But I prefer the linear nature of TMY-2 for shooting in the dark. I suspect that the linear toe holds shadow detail better than the s-curve of Tri-X. That combined with the finer grain makes it superior for push processing IMO. TMY-2 @ 1250/1600 in XTOL looks really good.