The Russians claimed 275 hits. The centrifical engines seem to have been more immune to damage than the axial ones in the Sabres and other US aircraft, as they have a lot fewer incidents cited of engine failure (same with the Australians, who had a similar type of engine in the Meteor).
Most damage to MiGs occured if the pilot was hit or something in the hydraulic system, as that would burn very quickly. A number of MiGs made deadstick landings at their bases with engines that shut down due to damage, but then they were close enough to glide home from 30,000 feet whereas USAF aircraft were lucky to get out over Gulf of Korea and punch out.
But Gabreski was the one who whistfully noted that even if you shoot up your entire load of ammo on a MiG, they don't burn at 40,000 feet.