Live recording is great if folks can get though the songs without mistakes. A more natural feel and vibe with people playing off and reacting to each other. Even in the most subtle ways, it still sounds more realistic than the "assembled" records.
But, you either need a studio with lots of tracking rooms and isolation or you need basically flawless performances. If you are going to be doing punches and fixes, then you need to have things isolated enough that you can redo a track without the background jumping in and out.
My personal favorite is to record a live guide track, and then go back and re-do the individual instruments with care put into getting each one to sound as good as it can. Which usually means putting the drums in the big room. Same with guitar amps. You can close mic something in an iso booth, but it doesn't sound the same as getting an ambience mic in a larger space. Those Zep albums sounded the way they did because they had the physical space to let each instrument breathe, including Bonzo's kit.
Another thing is to make up a computer sequenced guide track with the basic beat, a bass line, and some sort of chords to set the framework of the song. Then each person plays along to that. This keeps things in time and the arrangement of the song set without having to try a lock into a sterile click.
For any of these "assembled" techniques, you should still be comfortable enough with the song, having played it live enough to work out the little dynamic contrasts and things that make the song go.