No one here will be able to prove that the F-35 will have a decent range advantage. However, if you compare percentage of fuel weight over clean all up weight, it gives a good indication on their range capabilities.
F-35A - about 45% of total weight is fuel.
F-22A - about 37% of total weight is fuel.
All else being equal, the F-35A should have a decent range advantage over the F-22A. The technologies in their engines should be about the same generation. These figures will vary for the B and C versions of the Lightning.
There is absolutely no doubt that the F-22A will be superior in air to air, being the bread and butter of the USAF. Among other things, supercruise ability will be better than the F-35. AAM weapons load is double. Even the radar will likely be better optimised for air to air. Yet, the F-35 cannot be too far off since the USN needs to have a credible air to air capability.
As for the F-35 being able to carry 14 AAMs, look at this
link. External AAM carriage in future air combat is highly unlikely against modern air to air threats. Now if the air to air threats don't exist, why would they need 14 AAMs? It is thus unlikely that the F-35 will ever be able to carry 14 AAMs unless certain international partners are willing to fund this development.
Given the priorities, I would opt for more F-35s. The Lightnings will be able to do the job most of the time.