The F-104, being an interceptor, has the higher maximum speed, and better high-speed-performance.
The MIG-21 is a dogfighter, and has better subsonic performance, and tighter turn radius.
In a Dogfight the MIG-21 wins easily. Even a MIG-17 can take on the F-104 in an outright dogfight and win (!).
That's why F-104 pilots were trained to use their high-speed performance, making slashing attacks on their targets, without evolving in a real dogfight - after all, it's all about using your advantages against your enemy's weaknesses.
About Major Striker reference to the Israeli Air Force's experience with the MIG-21 - During the Six-Days-War, The French Mirage IIICJ (the model used by Israel) was the lesser fighter compared to the MIG-21 - especially in maneuverability , but the differences were somewhat minor.
However, a year earlier, in June 1966, an Iraqi defector, flew a MIG-21 to Israel, allowing the IDF-AF to train it's pilots against the real thing, learning it's weaknesses, and ultimately conquering the skies.
On another note:
1. TankGunner claimed an expert F-4 pilot can down a novice F-22 pilot - that's not so true - I don't know what is your definition of a novice pilot, but a below average F-16 pilot can quite easily down an ACE F-4 pilot, simply because the F-16 can literally fly circles around the F-4.
2. Tigerhawk claimed the F-15 won't stay in service for much long – Both the Israeli and Turkish (as well as other) air-forces are still operating F-4 Phantoms, and the IDF-AF intendeds to keep using them for at least 7-10 years more (I don't know about the Turkish or other air-forces).
So what makes you say the F-15 (and specifically the brand new F-15-E, -I and –K models) are soon the be withdrawn from service?