A few years ago, I flew a series of duels against one of the game's better F4U drivers. I flew an F6F-5. The fights were pretty much a draw. Bored with that, I switched to a 109F-4.
The fights were no longer even. The 109 completely dominates the vertical. The other guy could do nothing, but bleed E and then have to evade. There is one thing to remember about 109s. Flaps out, nose high, WEP engaged.... It will not roll to the right. You either have to reduce power, or simply go left instead. If you don't, you'll hang there and lose any advantage.
More recently, I flew the same type of duel with another Corsair specialist. Avoid getting hit on the second merge, and the 109 will soon have the advantage. The F4U-1 series simply cannot hang with the 109F in the vertical. As opposed to this, years back I flew many duels with Urchin. He flew a Spit16 and I had an F4U-1D. Every fight, I was able to get guns on him first (tho not always kill shots). That's because you can bleed E much faster and beat the Spit on the first and second reversal. The problem that would arise was, if I didn't kill or badly damage the Spit early, Urchin would take the fight vertical and gain a significant advantage.
So, versus the F4U, fight your fight. Fight to the 109's strengths. Fight up hill, and be careful not to hang in space, nose high and flaps out. Keep the fight turning left whenever possible. Do these things and as mtnman pointed out, there is very little the F4U can do to counter. Just remember, that like any other fighter, you'll have to fly the 109F often to learn its behavior and capability.