Question about live albums

So I thought of this after listening to Live at Reading, the new Nirvana album.

If a band puts out a live album or a live song on an album and later, a much better, cleaner recording from a different source is found, should that recording be put out separately or should it be inserted in place of the previous recording or recordings?

Specifically as an example, I'm referring to Tourrette's from the album which was previously released on Muddy Banks of the Wishkah but here sounds excellent like it came straight from the soundboard and on the previous release sounds like an audience recording.

no live has its own glory

Many live recordings do sound better then the studio album (to me) but I think that has more to do with the fact the band has had more time with the song to improve upon it plus you have the enegry from the crowd on your back. After hearing Prelude/Angry Young Man live from Carnegie Hall I can't listen to the studio version because it sounds so inferior.

I was talking about sourcing. As in like, hey, we've had this live album for years and we just found a better recording from the board, not from the audience. Is it better to just sneak it on for a rerelease or put it out as a separate album/single.

Again, my primary example being that the version on Tourrette's Nirvana's live at Reading is the exact same performance as on Muddy Banks but from a different source.

Like if the Beatles released Live at the Hollywood Bowl and then found a better source, is it better to supplant the original recording or release a separate album called "Hollywood Bowl, stage left" or whatever? And I'm not talking from a marketing, push as much crap as possible perspective.