Back on topic.. The combat record clearly shows the Mig-21 defeating the F-104's in their engagements. The two are very similar in their statistics and one could attribute the winner as being due to superior circumstances or pilot skills. In the few instances where the two fighter craft were engaged in combat, it seems the situations favored the Mig-21. The F-104's were attacked by Mig-21s while they were engaging other enemy targets. In one instance the F-104s were finishing up an attack behind enemy lines on ground targets when they were jumped by Mig-21's.. One F-104 escaped. In another instance the F-104's were attacking a bomber formation that was being escorted by Mig-21's.
In one of the Mig-21's F-104 kills, it began the engagement on the six o'clock position of the F-104's engaging the enemy ground targets, which is hardly a fair fight. In the instance of the F-104's attacking the bomber formation, one of the F-104's pilots launched a heat seeking missile while traveling head on- the first indication of a novice pilot flying the F-104.. The F-104's were later shot down while trying to out turn the Mig-21's. This was the second, fatal, and last indication of the lack of flying skill and knowledge of the F-104 pilots.
Since WW2, history has generally favored the faster fighter in equal combat by skilled pilots due to the fact that the faster fighter can dictate the terms of the engagement and use it's superior speed to "extend" and either escape or re-engage on it's own terms.. one of the more famous instances of these tactics were those used by the "Flying Tigers" (Starlancer fans will recognize this squadron) to rack up an astounding kill ratio vs. more agile enemy fighters. The statistics of the variants shown on this thread show the F-104 as being the faster fighter, giving it this powerful advantage. Given these statistics, an F-104 pilot can nullify the Mig-21's superior turning ratio by simply avoiding a turning battle.
Unfortunately, the F-104 wasn't particularly effective at head on combat since its guns weren't superior (possibly inferior?) to the Mig-21. Since its missiles were heat seeking, it would need to maneuver it's way to the enemy fighter's six. This would be very difficult vs. a Mig-21. Likewise a Mig-21 would probably have a slightly harder time maneuvering onto the faster F-104's six IF the F-104 pilot wisely refused to engage in a turning battle.
In combat where all things are equal, the F-104 pilot would dictate the terms of the combat, but vs. an equally skilled Mig-21 pilot would have a tough time gaining any advantage vs. the high calibur guns the Mig carries as it engages in the continual head on engagements that could result. The question could be whether the F-104's speed advantage is enough to travel outside of the Mig's missile range by the time and distance it takes for the Mig to turn around. The F-104 could have a slight advantage as it could escape with more ease due to its superior speed while the Mig is trapped in combat. The F-104 may also be able to develop an altitude advantage by using its superior speed and thrust. The Mig would have time on its side though since the F-104 would run out of fuel faster.
These fighters are so comparable that it might boil down to the economics of which fighter is cheaper to build and easier to maintain. Unfortunately for the F-104, it had a terrible reputation for accidents.
The Mig-21 would appear to be a better choice for missions such as bomber escort, where it could use its advanage in range and use its maneuvarability to orient itself on the six of the fighters attacking the bombers. I think the F-104 would have a slight advantage in 1v1, all things being equal.