hanoijane isn't alone in his (her?) low opinion of the F4 when compared with the Soviet fighters of the same era. John ("forty second*") Boyd, the USAF pilot who was without peer in his day - (look him up on Wikipedia; an entertaining read, where the "forty second" nick name will be explained) - using computer modelling, proved it was a dog against the MiG21, with it only maybe anywhere near equal to it below 15,000', and the majority of USAF and USN crews who defeated the MiG in the F4 did so using tactics devised very, very scientifically by Boyd using Pentagon computers - unofficially (and much against the wishes of his superiors, to the point where he was court-martialled for stealing over $1 million of computer time devising tactics that saved the lives of many, many American pilots).
The poor bastards sent into North Vietnam in the F105 were literally dicing with certain death against the MiGs (even the earlier -17s and -19s), for the Thud couldn't even outrun the -21, and the few who survived a one on one with a MiG did so using a last ditch 'flat plate' manoeuvre, again devised by Boyd, where they threw everything out and killed most of their energy in an attempt to make the MiG overshoot them. (Yeah, I know... if the MiG had a wingman, the Thud driver was then in a not-nice-place, which all too often resulted in a long stay for the Thud driver in the Hanoi Hilton.)
And as orca says, the J-79s and their massive black smoke trail (along with the F-4's massive size) was a dead giveaway during ACM. Another huge problem (until the 'E'), was the lack of a gun and the fact that the AIM7 and 9 were both very unreliable.