It seems to me that studio recordings often suffer from being over-produced. On the other hand, live recordings often suffer from being under-produced. In light of that, my personal preference is for a studio recording that could be mistaken for a live recording or a live recording that could be mistaken for a studio recording.
IMO, live recordings sound best when they emulate studio recordings, i.e., when they pay attention to microphone placement, track cleanliness, and mixing precision. Conversely, studio recordings sound best when they emulate live recordings, i.e., when they pay attention to acoustical setting, performer interaction, and a feeling of improvisation.
The best live recordings give you the feeling that the musical event you are hearing is happening now, and will never happen again. The best studio recordings give you the feeling that you have the perfect seat for the musical event. To have both feelings at the same time is a special experience. Hence, I like studio recordings that sound live or live recordings that sound studio.
Bryon