The thing is and this is coming from a neutral stance (and admittedly ignorant)
Lion-O doesn't have enhanced strength or invulnerability does he? He's just at whatever normal strength his species would have (but at the peak like a professional athlete) isn't he?
The sword of power was not split in two during combat, and as far as we know it can't be split in two by just some guy pulling on it right?
I don't know much re the trials of lion-o
Even though this is a he-man website the points (queries to a degree as I do claim ignorance on some issues) are factual to the characters. it's like I prefer The Rock over Bret Hart any day, but Bret Hart can out wrestle the Rock handily. (actual wrestling) when they are both at their peak. In my opinion that is. and this is someone who NEVER liked Bret Hart.
putting it to a vote would just be a popularity contest, but doing it like deadliest warrior, he-man wins (as you HAVE to allow for EVERY feat of strength and ability that both characters have displayed outside of parodies and use the established rules of both universes. so as Lion-o can controlcats it would stand to reason he control's BC, but as it's been shown that battlecat is seemingly immune to this (beastman can't control him) lion-o's power here wouldn't work.
Also have they SHOWN Lion-o control cats before? (legitimate curiousity)
so a clash of swords the sword of omens shatters, a test of strength Lion-o loses out, lion-o is probably more agile, but we've seen he-man run fast enough to create a vortex of water. (ridiculous or not, rules of deadliest warrior allow that speed)
what feats has lion-o done? (ridiculous is fine)