Is there anything better than live recordings?

Depends on the quality of the recording.  I'd rather listen to a great studio recording than a poor live recording.  

All thing being equal in terms of quality of the recording.

Disagree 100%. A lot of great music is created and built in the studio, and was never intended to be performed live but rather heard on recordings. 

Disagree 100%? That's a lot.

Always very happy to find a live recording where the dynamics is kept.