Morrowind on the original Xbox doesn't run as smooth as it does in a good PC (and by today's standard most PC are great to play Morrowind). The 360 emulates the Xbox and as far as that goes it does a good job at being just as slow as it was on the original.
But Morrowind on the Xbox was my first game-love and although I would now recommend getting the PC version + Graphic Extender it is better then no Morrowind at all.
P.S. has anyone played Jade Empire or Fable on the 360? Both games look much better then on the original Xbox. Especially Fable which is much sharper and more clear on the 360. In fact it looks much better then Fable II and III.