Regarding MMA fitness, MMA has considerable, perhaps, primary, importance toward cardiovascular conditioning. But, let's not completely downplay the anaerobic aspect. You do need to be strong. You need explosiveness. There wouldn't be strict weight classes if it was just all skill and cardio. There are a lot of top guys who are "jacked", maybe not to BB standards, but most are natural and would rival a natural BB'er.
And now my societal, adolescent fighting analysis:
In layman's, the BB'er has the general advantage over a weaker person of similar fighting skill. However, he will lose this advantage if the other weaker guy has better cardio and confidence (does not fall for visual intimidation factor) if the fight carries on and is not stopped soon by KO or submission, or other means. I've seen it first hand, and I have seen the strongest, toughest guys, be humbled by oxygen deprivation. It will make anyone say "I've had enough".