From my experience, I remember the following things when I'm listening to another band's live gig or album, and i find differences:
1) The studio is a controlled environment.
A live setup has a lot of factors. When I record in the studio, I go through a preamp that goes to a line-in for digital tracking. From there, the sound can be digitally enhanced. In a live setting, I've had the sheer "joy" of having to play anywhere from a PA line-in to a really ratty practice bass amp that doesn't even have a brand name. It's difficult to emulate my bass sound on the album with stuff like that. If we play a gig where there is a nice bass amp, I am very thankful. however, that's not the case with a lot of places nowadays.
On the other hand, there are sound overtones and dynamics that are still difficult or impossible to replicate in a studio - some people have voices or instrumental sounds that simply are much better live.
2) In a studio, there is no ambient noise, no bad acoustics to make hearing other bandmates difficult.
A lot of times, there isn't even a decently working set of monitors. There are times when I can't hear the vocals, can't hear the rhythm guitar or can't hear the lead. A lot of times I have to rely on the drums. That's great for keeping time, but not so great when it comes down to the dynamics of a song. Playing live is a dynamic situation, and I make the best of it as I can.
Sometimes, too, the live environment can be better than a studio, in the sense that you get a room or bar that simply sounds good, or sounds good with your band's music. Panalo yun.
3) In the studio, one can get in the mood or one can create the mood to make music.
In a live situation, one makes do with what the place gives in terms of ambience. Recently I played a gig in a bar in malate that had a strobe light flashing non-stop. it was annoying as hell, and yes, we had to make do since the management apparently did not think of turning off the damn thing, or even want to, it seems.
But then, there are places that are simply a joy to play in, and make for a good atmosphere.
4) There are days, and there are days.
If I can't nail a song or a passage of a song in the studio in one session, most of the time, I have the luxury of coming back to it some other time. What you hear on an album is the best take for an instrumental or vocal line of a song. When it's live, there's no "net". But i find that a positive challenge, since it's a chance for me to either stretch out or play really tight, depending on the mood.
I'm not saying that it's impossible to nail a song or a performance right - a lot of musicians can do it, and it can be a matter of skill on the live performance, or a matter of what they did put down to a permanent record as the version of their song (or a song, for covers).
But it's also a matter of how the band's philosophy is when it comes to album recordings and live performances - some bands just think of the album recording as a guidepost to their live versions, others think of it as something they have to be able to do live; for others, the studio environment allows them to make the "ultimate" version of the song, but not necessarily a version that can be done live. Some don't even think about it - a recording is for the album, and they do something different live. For some bands, it's possible that the songs they made for an album are stuff they can't do live due to lack of live performance skills, or inexperience; for others, they put down a simplified version of a song on the album, which they jazz up live. Maraming permutations ang ganiyan.
There are bands that simply do not perform well live, but have great recordings. Other bands are great live, but suck in the studio. Some are good at both. and some are, well, not good at either.
So, take it as it is. Some bands are great live, some are great in the studio, some are good in both, and some aren't good in any situation. If you like a band's studio work, but not their live, then listen to the album, don't go to the gig. If another band is great live, but suck in the studio...well, go to the gigs, but keep a studio album of theirs as a reference, and hope that they come out with a live album. if a band is good at both, then by all means watch them and buy their album and make sure you have backups and videos, too. and if the band isn't good in both, then ask yourself why you're listening to them willingly (if you are). Maybe the songs are really good - and that's another thing entirely.