I can’t really say for popular bands, since I rarely see them, but for the sort of music I go to see, it really depends. For some bands, it’s impossible to play it like it is in the studio, maybe they have choral or orchestral parts, or certain members switch around instruments mid-song (like electric to acoustic guitar), or there’s layer or something. Sometimes it works to have some recording of the parts they can’t play live so it sounds like the album, and sometimes that ruins the energy, so they have to find a different way to arrange it.
Opeth is a great example of a band that will play stuff a fair bit differently live and that’s part of what makes their live performances brilliant. They regularly switch between electric and acoustic guitars, so they usually just stick with electric and have a softer sound for the acoustic bits, or for songs with lots of acoustic, they’ll play the whole thing on acoustic. They also tend to write very long songs, so they’ll tend to play it a bit faster and cut down on some of the longer interludes that may work on the album but could impact the flow of the set, and it lets them get in more songs too. They’ll often improvise parts or even entire solos. In fact, one of my favorite moments was in a mostly acoustic set they did, but at the end of a track, they swapped in an electric guitar and did a completely improvised extended solo. It was awesome.
Really, a lot of progressive bands can get away with that sort of thing, Dream Theater would be another good example, and they are also famous for improvising and extending solos or mashing together songs into medleys.
Other bands need to be as faithful to the CD as possible, and this is will often be the sorts of bands that play stuff much more focused on the technical and timing aspects. Thrash, like Metallica or Slayer, or djent or tech death just can’t do too much differently other than a little bit of improvisation in the same scales on their solos. This is also tends to be true for bands that have particularly catchy or well known tunes, they really can’t do too much with those tracks, even if they can mess around with others.
That all said, toward the idea of popular bands, I’d tend to believe that most of them get stuck performing them as close to the CD as possible, because that’s what the audience will likely want to hear.
Or something.
They played a few of their hits in a fluidy, slightly haphazard and flourishing way and it was still quite good and slightly comical.
