From what I have come to understand, alot of the F-86's abilities were brought up as a resposne to the attacks by MiG-15's and the inferiority on the P-80 Shooting Star against modern Soviet designs (which were bassed, as most know, on German Swept-Wing designs). However, as others have stated, the MiG 15 was more of an interceptor and piloted by relatively innept pilots (with some Soviet exceptions).
But like any military device, there were areas where one was superior to the other. The MiG 15 was generaly faster than the F-86 (depending on variant), but the F-86 was much more adept at turn and dive. So if the F-86 pilot wanted to run straight away, he would be a dead duck. But if he turned away, or dived away, he would have little worry. MiGs also preformed better at lower altitudes than an F-86, but their climb was limited.
Overall, in the multi-role sense, the F-86 was superior. But the MiG was a bit of a generation behind. Regardless, the MiG still played hell with the allies' less capable fighters.