It depends on the music, the idea and the production really.
It's what you're going for... personally I enjoy live more for the vibe, especially whilst performing. It is also never the same twice. However studio audio quality is so very important as it's a great medium to promote what could be live performances.
I am thinking of recording singles and albums live, pouring all my production skill into it to promote the music as a great, live performance and to also capture that live vibe which I, personally, love!