Having logged 1850 hrs. in the Phantom (178 combat missions in SEA from Korat Thailand and a tour at RAF Lakenheath) as well as having been operational in the F-14, F-15, and F/A-18 (Navy exchange tour with VX-4) and flight time in “other” aircraft I would like to add my bit to this discussion.
First as has been pointed out the F-4 was not designed as a fighter but rather a fleet air defense aircraft. As such its primary mission was intercepting in-bound bombers. Having said that, it did a remarkable job in the fighter role given its original design requirements. Two things relative to its performance against the Mig-21: it could indeed turn with a Mig-21 at low speeds if approach flaps deployed (a trick not normally taught or condoned at the time). The Mig-21 could not accelerate out of the slow speed situation and it was possible to actually turn in front but above the Mig-21 in a turning fight with ½ flaps as he could not get the nose up to get a shot. Secondly if you could kept the Mig-21 a bay for any length of time you would run it out of gas. There were many times when we would log only 20 minute flights if afterburner was used extensively. The other issue is the pilots that were flying the F-4 over the course of the war. With one tour of duty being the norm, some of my squadron mates in SEA were newly minted F-4 drivers coming from bombers or transports. I takes more than a 3 month course to become truly proficient as a fighter pilot. In addition, as has been mentioned also, we were unable to use the one advantage we had which was better avionics and missiles (from the fleet defense mission) because of the requirement to visually identify the target. This generally put us into a dog fight position at the start. And yes IMHO the Mig-23 was not as much of a threat as the Mig-21. Interestingly you could not move the Mig-23 wings when maneuvering above 3 g, unlike the F-14 which automatically scheduled the movement based on air data inputs and at any loading. It was fast however and could run down a B-1 doing low level ingress at 550 kts. thinking they were untouchable.
As technology progressed the F-15 enjoyed both an aerodynamic and avionics advantage. The F-4 is close to neutrally stable at 400-500 kts. (a real credit to the demonstration teams who flew the F-4) and had a tendency to depart at high angles of attack if not handled with care. It was very interesting to see the members of USAF test pilot school classes after mine enter the school with only time in the F-15 or F-16 get into the F-4 and attempt to fly it with precision. I vividly remember my first flight in the F-15 when I was demonstrated a tail slide in the aircraft. The ease of flying the F-15 was one of the keys to allowing single pilot operation as you could concentrate on running the avionics since the aircraft was so easy to fly. In addition regardless of what some folks have said being in a Mig-21 (or F-4 for that matter) “snug in the metal cockpit with mirrors to cover six” is not preferable to the visibility and panoramic view from the F-15 or F/A-18 when the enemy is within visual range. And the 1/8 inch metal isn’t going to stop any projectile.
Combat tactics moved on as the F-15 entered service. Although we still enjoyed doing one-v-one dog fighting it became obvious, as Red Flag pointed out, that “shooting the boggy in the face” was the best approach to arriving home alive. The focus became using the avionics (and other systems) to obtain an ID on the boggy. The whole idea was not to get into a turning engagement as this tended to attract unwanted attention like flies to s__t.
Now on to the F-22 and the next technology, stealth. Without getting into this area too deeply it is the next evolution in shooting the boggy in the face. It becomes dueling radars and dueling missiles - who can get situational awareness first and who can get off the first effective shot at the longest range. Sensor integration is the name of the game. The number of missiles matters as quantity has a quality of its own. And an IRST is of great value for that additional passive information it provides. It is still tremendously maneuverable if it has to but that is not the preferred method of employment.
Next up - high power lasers and unmanned fighters but that’s for another thread.
So even if you could afford to upgrade an F-4 with modern avionics you still would have the aerodynamics of the basic platform and the visibility of the basic platform. In addition, you would have to up-grade the ECS and other system to provide the liquid cooling and electrical power required for the avionics and you would still have the maintenance issues (believe me the F-4 was not designed to be nearly as supportable as current fighters). I enjoyed flying the Phantom but if I had to go to war today please put me in an F-15 or F-22 regardless of what avionics you put in the F-4