I could be wrong but I believe that The P-47 once fitted with the paddle blade prop could out climb the BF 109G. The 109 G was heavy and sluggish, they should have stopped at the 109 F, the best of the lot.
The prop made a difference in climbing, but took away a little speed. The former was more important though than the latter, especially since the T-Bolts were meant to engage with the Messerschmidts, not escape from them!
All the armor and armament of the Me 109 G made it difficult to handle, captured Gs were remarked on by Allied test pilots to have the "nastiest handling characteristics imaginable". But there was a reason for it. While the F model was around, the Luftwaffe still reigned European skies, daylight bombing wasn't in full swing and the USAAF Flying Fortress and Liberator fleets weren't yet over the Reich. The F had great handling qualities, but was only armed with one cannon in the snout and two machine guns on the cowling. Try shooting down a B-17 or B-24 with that, especially if you only have a couple of seconds (and a Lightning or T-Bolt at your tail) and your one shot better be lethal to the four engine monster!!! The F's firepower was fine in a dogfight with another fighter, but even when it was introduced it split Luftwaffe pilots right down the middle.
Luftwaffe Experte Werner Mölders rejoiced at its agility and the lighter armament ("finally, people have to aim again, not just spray bullets"), but he wasn't an active fighter pilot by then anymore (and crashed to his death in an Me 110 soon after without apparent Allied influence), but many active Luftwaffe pilots were aghast: "where the Allied fighters have more and more armament, we get less!", the F had one cannon less than the E (which had two wing cannons rather than a snout one, those wing cannons would return for many of the various G variants, especially as the war progressed, some Gs sported even three 2 cm cannons plus two cowling machine guns, other models featured two 3 cm cannons plus machine guns, German pilots referred to these heavily armed Gs as "Kanonenboote" you'd better not dogfight with as even a T-Bolt was agile in comparison). Some pilots refused to exchange their Es against Fs as long as they still had spare parts for the older model and part of the Focke Wulf 190 A's initial appeal over the Me 109 (it came out around the time as the F) was its better armament (though its performance suffered above 20.000 feet, making it less than ideal to attack USAAF bomber streams which regularly flew at much higher altitudes, it took the water-cooled engine of the FW 190 D model to make the Focke-Wulf a high altitude fighter).
The G - for the reasons above - also had to have much better high altitude performance than the F, though getting it there did its overall handling no favors.
So the F was fine over the Channel when dogfighting with Spitfires or in North Africa where Hurricanes, P-40ies and Air Cobras were not a match for it as well as in Russia where most air combat took place at low altitudes against Russian aircraft that were technologically inferior. But I wouldn't have wanted to be the one flying it against several dozen B-17 all bristling with machine guns or against a P-47 twice as rugged and with heavier armament.
Most G models you see at flight shows today have the under-wing cannons removed as they hamper agility and reduce speed by about 30 mph.
The F or "Ferdinand":
The G or "Gustav", notice the telltale bulge behind the cowling:
