it wouldn't suprise me if they could compete with modern competitors in similar martial arts, but what they were doing doesn't seem likely to be similar to a modern boxer at all, the rules and equipment seem at least as different to moq fighting as an lpr fight would be(in different ways). Maybe what they did does look like the video posted here, or maybe they kicked more and it was like the older thai boxing films(i've read conflicting stuff today but kicking seems to be allowed). it could be true because the ancient greeks were tough muthas, but i doubt deaths were that common. an outskilled/sized guy could give up and forced stoppages due to injuries (particularly eye) would be pretty common i think, especially with the studded wraps in some of the pictures, those would ruin your face in a couple of punches.
Odysseus has a punchers chance. Then Ulysses considered whether he should let drive so hard at him as to make an end of him then and there, or whether he should give him a lighter blow that should only knock him down; in the end he deemed it best to give the lighter blow for fear the Achaeans should begin to suspect who he was. Then they began to fight, and Irus hit Ulysses on the right shoulder; but Ulysses gave Irus a blow on the neck under the ear that broke in the bones of his skull, and the blood came gushing out of his mouth; he fell groaning in the dust, gnashing his teeth and kicking on the ground, - The Odyssey Book 18