In general, the 109F is a much more capable fighter. In the FM2 you will be straggling to catch opponents unless you come with a lot of alt on them, or catch them during/after a fight with another. Those that you can catch, will be zekes, KI-43s and the super-Brewster, that can turn just about as well or even better than you. At the short ranges at which FM2 engages and the typical tracking shots you will get, the 4x0.5s do a good job and are easier to work with than the 109F single 20mm (the 7.62mm guns are for show). The main food of FM2 is probably spits that assume that they can out-turn anything. They will be wrong.
Perhaps the biggest thing you get in the FM2 that is missing in the 109F is durability. No radiator and very tough, the FM2 can take a hit and keep on fighting. Not very important in a duel, but in a furball this is meaningful. As a bonus, you can roll it from carriers which means you can use it in any fight, sea or land. It also has some JABO capability that the 109 does not have, but it is no F6F or F4U, so do not expect too much.
In the arena, 109F enjoys some "tag anonymity" - it appears as "109" till 1000 yards and everyone will assume that you are 109K or G14 at least. This helps the 109F a lot because 109K and 109F are very different planes in term of how they fight and opponents should treat them differently. The FM2 on the other hand appears as F4F till 1000 yards which makes little difference to your opponent.