@Dang Spot
On this page http://www.guenstiger-essen.de/cps3faq/#231 CPS III FAQ quotes Billy Kane on the differences between the original CPS 3 version and the Dreamcast port. I can't make arguments about what Billy says, since I haven't spent nearly as much time with the arcade SF3-TS as I have with the DC version, but neither could I verify his suggestion about the sprite size, again, unless, he's referring to the collision detection bounds. Sprites in the DC version are pixel-perfect as evidenced by total absence of any ugly artifacts that would have occurred as a result of resizing. Sprites are untouched - that's a fact I can bet my head on.
If you ask me about the graphics in the port, I'd say that some background elements appear kind of odd. I can't quite put my finger on it... mmmm. they just don't have that fixed pixel matrix precision seen in CPS2 games. Instead it seems like it's a 3D engine game where objects are flat geometric plains with alpha-mapped textures applied to them. I didn't pay attention to see whether the CPS 3 Third Strike looks the same.

@Heinster1975
I don't know about the other differences, but the removal of the "unblockables" and the remixed opening theme certainly wasn't enforced by the limitations of DC. :-D

Anyway, if you're going for authenticity, the PS2 port of SF3-3rd Strike featured in the Street Fighter Anniversary Collection is arcade-perfect, I have been told.