Is there anything better than live recordings?

I much prefer studio rock recordings to most live ones.

Much depends on engineer, group, as many times they set up microphones and sound only relying on soundcheck without putting into account, the audience, microphones moving from original positions, the lighting, and many more.

100% DIS-agree!

Live performance is just that... it's a performance. An ephemeral event.

A studio recording is "A WORK OF ART".  It's a different thing entirely, and is to be admired in a totally different way.  Would you ever demand a real-time "performance" from a painter?  Would you ask him/her to make a painting in front of an audience, and then hold that painting up to scrutiny for years to come?  No, that's not how we judge and admire paintings, photos, or sculptures.

A studio album is a non-realtime creation, and is a completely different thing than a live performance.  Bear in mind that I'm NOT dumping on live recordings.  I love live Studio recordings.  I typically do not like recordings in front of an audience however, as most don't sound very good.  

"Live in the studio", which many jazz dudes (and some others) do, can sound amazing. Lots of pop music takes months to record, sweating over details and overdubs...some of my fave jazz musicians (or perhaps most of them) like Julian Lage or John Scofield record entire albums in a couple of days with astonishing results. 

There’s a difference between sonics and content. I assumed that the OP was addressing sonics as this is a high-end audio forum 

B.L.S. Black Light Syndrome | Bozzio, Levins, Steven's - Studio recording masterpiece 

The Pretenders | The Isle of View - Live recording masterpiece