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?
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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.