No reason at all to get a rebuild; K03sport would actually be a slight upgrade for>>>
you over your K03 - (I gather yours is a 2000.) You can get them very lightly used in fine shape for $200 or so, or a brand new one for $500 - that las figure is a bit of a guess on my part, but it's got to be close to that. "Rebuilding" could be labor intensive depending on what's being done, and may not be a good idea since tolerances are very tight in the small turbo - there may not be many parts you'd wnat anyone to try to repair, and doing so could be tricky. Get yourself a new or slightly used one. HAVING SAID ALL THAT, I would not expect yours to be even close to failing if it's had a halfway decent life, with regular, synthetic oil changes, no hard running when cold, and cool downs before shut off if its been run hard.
Believe all 2000s and some early '01s use the regular K03.
Not sure what you mean by "my Revo 93 program" - when you bought it, didn't you buy the one they list for your specific vehicle? Also, when these are installed, (either a chip that has to be installed, or I guess in Revo's vase they just flash it in directly) the installer has to select between an array of different versions of the Revo software based on your ECU number. There a number of different ECU versions within most model years, so the point is, a chip for a "2000 180 TT" will not work on all of them - you'd have to know if it was for ECU boxes ending in 'K', or 'L', etc. - those are just examples. But since Revo doesn't do actual chips, you shouldn't have a problem - whenever it's installed, they'll give you the right program for your ECU.
Turbo type isn't an issue, since that's factored into both the ECU's programming, and the code that Revo will install. Maybe their programming for K03 "sport"-equipped TTs is slightly more powerful, or has a slightly broader powerband, but that should be the only difference if any. Hope that somewhere in here I answered what you had in mind!
Re: So what's the difference between the K03 and the K03 Sport? Wheel trim? Porting? Both?
Try a search - it's been covered a million times here and on VW vortex 1.8T forum; I can't remember whether it is the intake or the exhaust turbine, but I believe the main or even only difference is that one of them is bigger on the K03sport.
All else being equal, MAX power would be a little higher on the K03 sport, and it has the ability to deliver a little better high-end blow. However, since these cars are engineered to deliver alot less then their max capability, the differences are not really significant unless you really tweak the cars and are staying with your stock turbo, whichever k03 variant that is. Obviously Audi was able to tune K03 powered cars to deliver the same 180 hp as the K03sports had later on becuse that was well within the efficiency range of both versions of the K03, and so only needed to tweak other parameters to deliver the same power.