IIRC, any instrument for RB2 or GHWT, or later, will work equally with "the other game" or later versions. It is backwards compatibility which is slightly problematic: I know GHWT drums don't work on RB1, and assume vice-versa as well, although as noted you can import most RB1 tracks into RB2 and play them in RB2 using GHWT instruments without trouble. A GH3 guitar should work on RB2 etc anyway, not entirely sure about RB1 but my best guess is it does work. I know a GHWT guitar DOES work with RB1 (I have the GHWT instruments, and have used the guitar to play RB1; drums don't work).
Also, for drums specifically, note that GHWT uses 5 lanes, RB only 4. GHWT (and later games) can detect if you are using RB2 drums, and will downmix the 'missing' orange lane notes (to mostly green, IIRC) for use on RB2 drums, which don't have orange notes.