Is there anything better than live recordings?

depends on how good the live performance sounds. 

There are no absolutes in audio.

There still is a lot of art in mixing down recordings. Even studio recordings have a lot of live sound to mix down. Without a doubt there are some very good live recordings. Better than a live show? Two different animals. 

All told, I enjoy the studio-made recordings in my collection more than the live ones. Even when they were meticulously assembled, a lot of the studio-produced LPs in my collection emotionally and viscerally  punch through. I just love my old Doors LPs. I just love my Byrds LPs, whatever era they might from be in terms of who was in the band or what genre they were pursuing. No shortage of emotional electricity in the Ramones' obviously studio-produced Road to Ruin.

Jeff Beck live recordings. Even though the engineers compressed these, the performances are amazing.