Neither. They should begin at Olympic athlete level, proceed past that to world-record-athlete level, and eventually reach transmundane status, where their methods are or should be mundane (at least IRL), yet they achieve results that go beyond the confines of mundanity.
The blacksmith who becomes so skilled, he smiths magic weapons with nothing more than knowledge, grit, technique, and material selection. This is a transmundane character.
A thief who begins by stealing the contents of nobles' pockets, grows to steal the weapons off the belts of devils, and ends by stealing the color of a fair maiden's eyes or his rival's shadow. Initially, it is simply a growth of purely physical, demonstrable skill. But in a fantastical world, where the thin skein of reality is more porous than our own, superlative skill transcends the limits of mere physical action, leaving us able to say what was done, but forced to admit we know not how.
And if players prefer not to have characters that reach such transcendental heights? Don't play epic level. Most players don't play epic anyway, or so I've been told!