TMX is a very fine grained film capable of very high resolution. It's got excellent reciprocity characteristics and a long straight line curve, so you can under or overexpose and still have a nice printable neg, or if you have a scene with a very wide brightness range, you can get it all on film and have something to work with at the printing stage.
Not everyone likes the look of TMX. The spectral sensitivity of TMX and TMY look a bit like B&W video or digital B&W straight from the camera--in a sense more linear than traditional films, but it looks less like a classic B&W look. Sometimes that works, and under some lighting conditions it doesn't matter, but not everyone cares for it.
TMX in its current version also has a UV absorbent layer (at one time it didn't), which makes it unappealing for most alternative processes, which are UV sensitive, because the prints will require excessively long exposures, and the same is true for silver chloride contact printing, which isn't as UV sensitive as most handcoated processes, but is more UV sensitive than enlarging papers.
Contact printing doesn't benefit so much from ultra-fine grain, so there's less reason for people who contact print to use TMX, though the reciprocity characteristics can be good for LF shooters who tend to shoot under conditions demanding long exposure times, when TMX may become faster than some 400 speed films.
While I still had old TMX without the UV layer, I liked it mainly for scenes that had a very wide brightness range, like this one--
http://www.echonyc.com/~goldfarb/photo/imviaduct.htm
When I used to shoot headshots in the 1990s, I also liked TMX, because with strobes the spectral sensitivity issues seemed less prominent, and the 35mm negs enlarged nicely to 8x10"--