I've been thinking about doing some street performance, but currently lack the means to amplify my electric without plugging it into the wall. There are some battery powered amps that seem to fit the bill and my price range, but I haven't been able to find them all in stock at local shops to try them out.
I play an Epiphone Les Paul Studio with a Gibson Burstbucker Pro in the bridge and a Seymour Duncan 59 in the neck. I'm primarily going for a heavy blues sound, but that's not all I want to do with it.
A couple of guitarists I've known have sworn by Pignose, but take that with a pinch of salt, I'm not a guitarist or busker. It's my understanding that they'll provide a heavy blues sound, though that's really up to you and your ears to decide.