Jan - I'm hardly the ideal person to respond, as I've done hundreds of rolls of Tri-X and only one of T-Max 400, but I seem to be the first...(posted 9145 days ago)If you're a beginner, you should definitely start out with TX over TMY. Don't take this the wrong way, but TX is nearly idiot-proof. You can overexpose or underexpose by two stops, overdevelop or underdevelop by two minutes, overagitate or underagitate during development, get your developing solution temperatures a bit off from each other, rate the film at the wrong speed when shooting... And you will nearly always get beautiful (or at least, darn good) results.
TMY is much more tempermental than TX regarding details of exposure and development and - although this is a minority POV - I don't think that the (slightly) finer grain and higher sharpness/resolution it provides is worth the trouble. Good old Tri-X, developed in good old D-76 (1:1, 10 minutes at 68 degrees), is still a wonderful combination, producing prints that are acceptably sharp with reasonable grain up to 8x10 from 35mm negs. And TX has a wonderful, slightly old-fashioned look that's great for most subjects. It's great stuff.
Anyway, personally I don't bother with TMY. When I need finer grain/higher resolution, I go with Plus-X or T-Max 100, both of which work far better for me than TMY. (I also like Agfapan 100 A LOT.) Obviously, YOU have to find out for YOURSELF what works best for YOU, but if you're just starting out, Tri-X is a far better place to start than T-Max 400, IMHO...