All else being equal? Then it would be an equal match.

A sword is a great weapon because it's versatile; you can have one that will thrust and chop and cut with it, but not do any of them spectacularly well, and that was the prevalent design during the 7th-11th centuries in Scandinavia. Axes were great at chopping and, if you can believe the sagas, not terrible at thrusting (with the 'horns' of the axe, as Skarpheðinn proved in Njáls saga)

Swords might give you an advantage of reach, if neither opponent were armed with a shield (if shielded, you could nullify that advantage fair well by advancing quickly behind cover) while axes are better at hacking through armour and shields (they move quicker and concentrate more mass and energy behind a smaller point than a sword)

A sword might let you weaken your opponent by a series of near misses and smaller cuts, slowing them down due to blood loss, but an axe is generally going to make itself known pretty well if it clips the target, even if it's not a dead-on strike.