Let's face it. This is a disappointing poll. Kind of like asking which of your sisters is the best kisser.
I'm going to give the edge to Martin, very narrowly, and it has very little to do with the Final Four run. Hey, we had a decent team that limped into the tournament, but happened to win four big games in a row. I'm not sure how much that proves about Martin's coaching ability. While it was a heck of a lot of fun to watch, I don't think it's as impressive as Fogler's accomplishment of winning the SEC title with a 15-1 record. That was several months of fun-to-watch. But the question wasn't which coach gave us the most impressive moment or the most impressive run. The OP asked who was the better coach.
I'm going to give Martin the edge since he has won more overall games (127 to 123) and nearly as many SEC games (54 to 57) through a not-quite-finished 7th season as Fogler did in 8 full seasons. That tells me his teams are more consistent winners than Foglers. Martin's style of play means that his teams are always going to be scrappers and are always going to be a threat to beat somebody. Even his teams' disappointing years are probably going to be around .500. If Martin's teams and Fogler's teams played each other 100 times, I think Martin's teams win about 55% of the games. Unfortunately, neither teams will go to the NCAA tournament often enough.