It’s possible that the Quake 3 engine counts vertices differently, I don’t really have much experience with models:-P Other people have run into this limit though, so obviously it exists in some form. Actually, googling a bit it appears the limit is per object (and a model can contain several objects).
As far as I know there are no fundamental differences between ASE and MD3 — both look identical and have the same (low-ish) performance impact. Apparently MD3 can’t be used for very large structures though — 512 unit limit?. ASE can be edited more easily and it’s a “real” model format, supported by many programs, unlike MD3 which is only used in some games.
BTW, you can also use OBJ format, but this
can be tricky to pull off. There are a few more formats listed in the model selection window of Radiant; never heard of anyone using them for UrT though.