Ignoring all logistics and technical issues completely, you end up with the air battles of the Korean War taking place 10 years earlier I think. Unless we also assume the ability exists to field large numbers of BVR (Beyond Visual Range) missiles and other guided weapons (along with the technologies to employ and maintain them, of course, which changes things completely) we would see aircraft similar to those developed immediately after WW2, which were generally in the high-subsonic range and continued to be armed with cannon and machine-guns.
In Calbear's thread on the Anglo-American / Nazi war the point is also made that piston-powered aircraft do not simply become irrelevant once jets are available. Especially in the early years of jet aviation, the prop birds have advantages in endurance and the disadvantages in speed are less acute than will be the case later on. In point of fact, jet strike aircraft spend a lot of their time at speeds very similar to those achieved by piston engine aircraft.
One way in which things might be different is that jet fighters might be able to contest the higher altitudes more effectively - this could make the USAAF daylight bombing raids in the later part of the war an even more expensive proposition. Conversely, they might find the reduction in loiter times makes it impossible to act as anything but point-defence interceptors.