Yeah you go to the options menu, there are three control configs if I remember.
Dpad + L trigger to run (Shenmue 1 controls)
Left Analog stick (allows to walk + run)
Right Analog stick (allows to walk + run)
I really found the xbox version to be subpar overall. They added glowing effects at night time that don't suit the game at all, a horrible blur during fights that make them almost unplayable, first person fights (which were awful), not to mention the English voice acting.
The only thing the xbox version has over the DC version is the camera, the extremely MINIMAL texture upgrades (water), and better load times. DC version as a whole, for some reason, felt like a better effort and I really enjoyed that game a lot.