I say live, but only because my two favorite STP songs are the acoustic (live) versions of "Crackerman" and "Sex Type Thing" from MTV Unplugged. STP sound killer on the Family Values Soundtrack, too, especially "Wonderful."
Overall, the studio sound is fuller and more dynamic and pitch-perfect, but if I can pick-and-choose, those unplugged moments will always be at the top of my list.