I always find this really interesting when it happens. Usually when bands drastically change lineups they ditch most of the old material, but some stuff sticks around. Either it gets tweaked in interesting ways to accommodate the different members. Or they play it the same way but it can't help but have a different vibe cus of the different members. it's like they're covers but not quite. Sometimes both versions are great in different ways, sometimes the new version of the band turns it into something new and awesome, and sometimes they totally ruin the song.
Obviously a big one is Collins-era Genesis. And I actually tend to like the Collins-led versions of the old songs a lot cus they often diverge from the originals in interesting ways (whereas the Gabriel-era live stuff is usually just extremely well performed versions of the same arrangements that are on the albums). And the CAS tour was a fascinating look into what Genesis songs sound like when they're sung without any charisma. One of the most interesting times with them to me is when Genesis played Solsbury Hill at their 1982 reunion show. it's rough and low quality, and not too different from the original, but has an interesting what-might-have-been vibe to it.
Gabriel also did a solo version of The Lamb title track on his early tours which is interesting too.
I also really like tracking the Barrett-era Floyd songs through their other lineups. Like the Ummagumma and Pulse versions of "Astronomy Domine".
Suggest other ones!