If the axe is a REALLY heavy and long axe, and the sword is a REALLY long claimore, i can easily say that there's not one better, all depend from the character ^^
Long sword as it is lighter and therefore more agile in the hands of a skilled user. Whereas a mighty axe is wielded with two hands and is relatively slow to swing and maneuver.
If both combatants are skilled, long sword 9 out of 10. The sword could easily deflect the axe blows and is fast enough to kill your opponent with a small opening. That would be why in history, you never saw knights wielding axes and almost always used swords.
Rankly, if it was me, I'd rather a knife, 'cause I would rather get them before they even noticed me. But, is I had to choose, I'd go sword, 'cause I probably couldn't lift a huge axe.
it really doesn't matter which weapon it is, it all depends on who is using it. If it was Maximus from gladiator, I would say the sword, but if it was Gimli from lotr, of course it would be the axe. so now comes the real question, Gimli with a battle axe, or Maximus with a longsword? It's a fair fight really, but I'd go with Maximus because, being a gladiator, he would be better at the 1 vs. 1 style of fighting.