I am definitely a fan of Yautja, and not so much one of Halo (though, I do admit the Elite are kinda' cool).
Either way, I'll try to be fair about this...
Strength-wise, the Elite have the advantage (they can flip a tank...)
Speed and fighting prowess may be about the same. Both seem to move as fast, and both species seem to have the same "life of training" culture. Though their fighting styles are very different.
Agility-wise, the advantage goes to Yautja. They can jump (and fall) much further, and move far more gracefully.
predxeno also makes a good point about the Elite having a heightened sense of smell. This could be a problem for a careless Hunter (Yautja have a strong musk). However, having hunted many different species of prey, one would hope the opposing Yautja would be accustomed to stalking downwind.
Both have a similar light-bending camoflage that renders them near invisible. Though Yautja tech has a standard issue thermal imaging visor that would make a stealth-minded Elite not as stealthy as he believes...
Comparing weaponry is something in itself, as Yautja tech is more designed for hunting, as Elite weaponry is better suited for more direct attacks. (with exceptions of course, Elites have sniper rifles, and Yauntja discs and plasmacasters can be used effectively close quarters)
The high fire rate of most of the Elites weapons can effectively give them the advantage, if they see the Yautja. But, plasmacasters can also lock-on to targets. And discs can be guided after thrown.
Each species choice of primary choice of melee weapons is also in the Elite's favor, as the lightsaberlike energy sword is more dangerous than metal wristblades -and also has more range.
Overall, this fight could go either way.
But, I'd say the advantage goes to the Yautja for hunting, and to the Elite in a face-to-face fight. (Far closer than the ridiculous Samus vs. Master Chief arguments...)
