I have only just seen this thread.
I like the F-106, but it is hardly comparable with the Phantom. The F-106 and F-4 were designed to fulfil different missions. Or rather, the F-106 was designed to fulfil only one mission, and the F-4 was designed to fulfil many, including a similar mission to the F-106. The F-106 was a pure interceptor, designed to engage Soviet bombers at high altitude as they entered US territory, during the strategic bomber era. After the nuclear powers moved into the missile era, the F-106 was left without its original mission.
The loss rate of the F-4 in air-to-air encounters against the Mig-21 in Vietnam is due largely to the fact that the North Vietnamese had the luxury of picking their fights, and using hit-and-run tactics with ground-controlled intercept. If the conditions were not to their favour, then the Migs would stay on the ground. Very few Phantom losses were in actual dogfights, and I believe that the Phantom and Mig-21 dogfight performance, particularly at low altitude, where most air-to-air engagements took place, was comparable, and the Mig did not completely outclass the Phantom. The primary mission of the F-4 in Vietnam was ground attack, and not fighter patrols. The Phantom began in USAF service in the conflict by escorting F-105s on strike missions, before taking over the F-105's role altogether. During Operation Bolo in 1967, a flight of F-4s lured North Vietnamese Mig-21s into air combat by making themselves appear to the air defence network as if they were less-capable F-105s. When the Mig-21s rose to meet them, the Phantoms shot down 7 Mig-21s without a loss. The Phantoms could have destroyed every one of the North Vietnamese Migs, if the rules of engagement did not forbid them from attacking aircraft on the ground.
The F-4 was carrier capable, being developed originally as a naval fighter-bomber and all-weather interceptor, had two crew, a bubble canopy, and could carry much more, and a much larger variety of, ordnance, as well as excelling in the ground attack role, which the F-106 was not even capable of performing. The F-4 was probably the greatest all-rounder of its era.