After digging out the big book of datasheets, this is what Kodak has to say:
Tri-X 400 is faster than 320. They have wide exposure latitude, and 400 is recommended (by Kodak) for pushing. Both are, of course, standard BW-process films.
I've used both at least once, and I don't recall anything special about them either, nor any special difference between the two. Of course, at the time, I was point-n-shooting, and not really aware of what I was looking for (or wasn't looking for, depending on how you look at it).
Oh, and apparently, Tri-X 400 isn't offered in sheet film. Hmm. There are also slight differences in the filtered exposure adjustment recommendations, development times, etc, etc.
Thus says the big book of datasheets. Anybody else with some information of a more useful character?