Personally, I don't think he was hamming it up... he's a showman and he does that flashy stuff automatically. If you look past that, you'll see a guitar player inspired by the musicians around him. His solo took Clapton's original (that's Clapton on the original Beatles recording) and takes it somewhere new. He obviously was familiar with the original, since he quoted it many times in his own solo.

If that don't impress you, nothing will