They've battled a few times as far as I know, but have their beams ever directly collided?
And if so, who came out on top?
In Adventures Of Superman 595, Superman and Darkseid fight on Apokolips. Their beams meet briefly at point-blank range during this fight and appear evenly matched. (The fight itself is interrupted by Brainiac-13.)
They collided here in Superman v Darkseid Apokolips Now in the Post Crisis era.
However New 52 Darkseid's Omega beams have been shown to destroy planets, Superman's heat vision isn't remotely as powerful.