The main gripes about the RSX are the leather not being that high quality (which was fixed for 05-06), the gears grind (a problem i've never had but is very widespread, supposedly it was fixed for 05-06) and the tires (unfortunately the 06 still uses the crappy Michelin all-seasons, they're just .5 inches wider than 02-04).
I don't see you having any problems. One downside of the 05-06 RSX is the lack of aftermarket parts compared to the 02-04 (although there's still quite a bit you can do for the 05-06).
The Integra GS-R is more of a competition for the base RSX. The Type S is just slightly outperformed by the Integra Type R.