The whole cover sounds rather digital to me, not just the distortion.

This is pretty much the commonly regarded exemplification of "digital" though. http://www.youtube.com/watch?v=Tb0N9Cbs6pY&feature=related
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There's a distinction that needs to be made here: digital and solid state are not the same thing. The first video posted sounds like a solid state amp. The second one sounds digital. Although the first one does have a slight digital resonance to it because of the Korg AX3000G processor.
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