Actually, I don't think it would have done that much better. Okay, it had the gun, but not the training. It would still have been lured into the MiG trap. F-106 is an interceptor remember, this has huge impact on the way it is used. It would have been at too close a range to use its missiles. AIM-9B was crap, whether on a F-106 or F-4. At least the F-4 had two sets of eyes in the cockpit. The F-4 could and did also outrun the MiGs. And with no huge bomb loads on the F-106 or rocket pods, you would also need more bombers. So I don't know if it would have made a difference.
My dear friend, the F-106 never carried the Sidewinder. It carried the Falcon missile, which in early models was far superior to the AIM-9. Since, most fights were close in, the difference in radar efficiency, wasn't a big factor in the equation. About the visibility, in the sixties, the -6 aquired a bubble (!) canopy for better pilot vision, but i agree with you it lacked the second pair of eyes the F-4 had.
It would never be an all around player like the F-4, no bombs could be carried, or anything air to ground, so its use would be limited as an air superiority fighter. It was maneuvrable, not as an F-5, but better than the F-4, due to its lower wing loading. A loaded air to air -6, had less drag than a F-4, and to the eyes of the enemy, opposed an unkonown factor. U could not tell, if it was loaded or not.
But, as with the B-58, it never saw action. The B-58s were sold as aluminium and the -6 are ending their days as drones. Did i say B-58? i'm gonna put a new thread........