The P-47 Thunderbolt and the P-51 Mustang fought side-by-side with the Allies in World War II. They even divided the job of kicking Axis ass between them by the end of the war. The Mustang became known as an escort fighter, while the Thunderbolt took more of a role as a fighter-bomber.
That said, how would they have fared in a head-to-head fight? It might not be as fantastical as everyone thinks.
The Nazis captured several P-51s during World War II, usually by repairing planes that crash-landed. They also captured some P-47s. This means there was a chance (albeit small) that a P-47 and P-51 could have ended up fighting each other.
The P-51 and P-47 sit side-by-side. (Photo by Alan Wilson via WikiMedia Commons)
Each plane has its strengths and weaknesses, of course. The P-51 had long range (especially with drop tanks), and its six M2 .50-caliber machine guns could take down just about any opposing fighter.
In fact, the P-51 was credited with 4,950 air-to-air kills in the European theater alone. During the Korean War, the P-51 also proved to be a decent ground-attack plane.
That said, the secret to the P-51's success, the Rolls Royce Merlin engine, was also, in a sense, the plane's greatest weakness. The liquid-cooled engine was far more vulnerable to damage; furthermore the P-51 itself was also somewhat fragile.
By contrast, the P-47 Thunderbolt was known for being very tough. In one sense, it was the A-10 of World War II, being able to carry a good payload, take a lot of damage, and make it home (it even shares its name with the A-10 Thunderbolt II).
In one incident on June 26, 1943, a P-47 flown by Robert S. Johnson was hit by hundreds of rounds of German fire, and still returned home. The P-47 carried eight M2 .50-caliber machine guns, arguably the most powerful armament on an American single-engine fighter.
The "Jug" shot down over 3700 enemy aircraft during World War II, proving itself a capable dogfighter.
P-47 & P-51 — Flying Legends 2012 — Duxford (Photo by Airwolfhound)
Which plane would come out on top in a dogfight? The P-51's superior speed, range, and maneuverability might help in a dogfight, but the P-47 survived hits from weapons far more powerful than the M2 Browning — notably the 20mm and 30mm cannon on German fighters like the FW-190 or Me-109.
What is most likely to happen is that the P-51 would empty its guns into the P-47, but fail to score a fatal hit.
Worse, a mistake by the P-51 pilot would put it in the sights of the P-47's guns, and the Mustang would likely be unable to survive that pounding.
All in all, we love 'em both, but we'd put money down on the Thunderbolt.