"They all have ranges of 10-18 miles depending on altitude."
Actually, in SOME flight profiles(head on close, diving flight profile), AIM-9X has a range of 25 miles or so(according to the unofficial gossip this l'il ex grunt has collected).
BTW, launched at Mach 1.5 from the Raptor(typical max supercruise speed), the AIM-9X and AIM-120 BOTH have roughly 30% greater range than 'normal' due to the higher initial velocity of the AAM- much less fuel is expended in acceleration, and is instead burned for sustain.
This is also the reason why AAM derived SAMs have much shorter range than their air launched cousins.
The F-14, 15, 16, and 18 must be subsonic to launch a missile. The Raptor is the first US(and i think ROW too) fighter capable of supersonic missile release.
Just another of the HUGE advantadges the Raptor will hold over all comers.
As far as the AIM-9X/Python argument, the AIM-9X is reputed to have a 90g manuevering threshold, is +/- 90 degree HOBS capable, and has an UNMATCHED 3rd generation IIR seeker.
AIM-9X does not chase the heat of it's target, it chases a high resolution 3D image of it's target. That means IR flares are utterly worthless against AIM-9X.
According to the pilots that have been involved in testing, AIM-9X has no rival in the world.