My $0.02:
It really is the fighter, not the style.
I think in the early days, it was pretty clear that in the style vs style fights, BJJ and other grappling styles did better than the striking styles (with bjj doing the best). It wasn't until Maurice Smith (a kickboxing champion with a lot of ground training under his belt) came around that mma in the US got a standup striker for a champ. That was 4 years after BJJ and wrestling had been pretty much king of MMA.
I don't think this was so much due to the art itself as it was the BJJ guys from brazil had been fighting in challenge matches for quite a while and were used to dealing with punches and kicks. They'd learned to adapt their art to the fight and make it work for them.
Now, I think some styles train a bit more...... I don't want to say realistically, because it is a sporting duelistic atmosphere, but with more pressure and in an alive fashion so their practitioners are more used to making their art work against pressure. Arts like Muay Thai, boxing, wrestling, the other grappling arts, tend to train harder and with a fully resisting partner. Other styles, like most TMA schools, train with a "helpful" partner that means they don't get to work with failure and learn how to make their stuff work against different kinds of resistance.
I think if you train realistically, against fully resisting opponents, you can learn to make most styles work for you.