I love them both. To me it all boils down to how much time you have for said recording session. If you are recording in a home studio with nothing but time to perfect parts, sounds and percussive overdubs then yes, the studio is an amazing place to be. However most of the time I find myself on sessions where you have an hour to record five songs. with charts (if your lucky) written by a composer who has obliviously never even seen a drum chart, playing equipment that sounds like an assortment of cardboard boxes that the engineer swears sound great through his gear.
Considering how costly “studio time” is, I have found myself in more stressful situations then rewarding ones. You dont ever want to be the reason someone has to dip into their pockets for the dreaded OVERTIME!!!
I suppose I would have to go with live. The studio will never be able to duplicate that slight adrenaline rush that comes from performing to a real live audience.