Les Paul would win that discussion everytime. Now the real question is which kind of Gibson.
My preference for overall use is the Les Paul. But I used to have an Epiphone SG that had some mods done to it and it played really nicely, got that nice Chunk when paired with a Marshall JCM 900.
A few times a month I like to torture myself and go into Guitar Center and play the Epiphone Sheraton II through an Orange Tiny Terror..it responds really well to attack and the volume knob on the guitar.