In my Classic Rock band I listen to the original (or best known) version of a song and do my best to emulate everything on it. I'm nowhere near good enough to do this, but by aiming for the very best copy of a drum part that I can, enough of it makes its way into my performance to "pass for" the original part. It's like that saying, if you aim for the stars and don't hit them you'll hit the moon instead. There are parts in some songs that are not negotiable. FYI, we don't play Rock And Roll by Led Zeppelin, but if we did then the drum solo at the end would have to be in there. If it wasn't then we wouldn't do it.
In my Glam Rock band my approach is different. There are a lot of shuffles and floor Tom work in some of these songs and as my band is taking the music from the period and rocking it up, these don't quite "work" in the context of the band so I come up with alternatives. To take my last point from the previous paragraph, the snare and bass shuffle from Ballroom Blitz is present at the beginning of the song and the breaks within the song, however I use snare and hi hat between these points and don't re introduce the shuffle the way it was done in the original. Partly because it fits our band, mostly it's because I'm not fit to carry Mick Tuckers stick bag
We also totally alter a lot of songs with stabs, stops and key changes but that's more to do with our bands identity, if we were more "serious" and doing the tribute or corporate circuits then we'd be as authentic to the originals as we could. Of course now with YouTube we can also see that even the band's themselves often played live versions radically different to their recorded versions.