I think the F-35 is a true "Jack of all trades, master of none". Or rather, a brave but futile attempt to downscale F-22 in size and in cost, at the cost of capabilities.
Sure, it's stealth, but it's still no F-22 or F-117. It carries a pitifully small weapons load internally (four AAM's, but only of certain size - can't fit four AMRAAM's, has to be two plus two Sidewinders). Add weapon pylons, and suddenly it's not so stealthy anymore. And even with the extra pylons, it still can't carry very much compared to the planes it is supposed to replace. The 25 mm cannon might be more powerful than the venerable M61 Vulcan, but it's still no tank-busting cannon like the GAU-8/A of Warthog. Without drop tanks, the range is also nothing to write home about. No supercruise, although the thrust/weight ratio is decent in the CTOL version. Instead of having completely vectored thrust like the Harrier, the STOVL versions use a liftjet which is just so much dead weight when not taking off or landing, plus makes the plane bigger than it would be without.
Unfortunately, there has been few reports on mock dogfights against other modern jets, but on paper it would seem that it is clearly inferior to the F-22, and that the Eurofighter would be better in air-to-air role (maybe also in strike role). I hear the manufacturer has been claiming that with the helmet-mounted display (and supposedly "360 degree view") and such, manoeuverability would no longer be an issue, but I think we heard pretty much the same story slightly before Vietnam War. Less wealthy nations would probably ignore both and go for Su-35BM or the "future aircraft" MiG tries to build for the Indian Air Force.
The wild card is the development of next-generation UAV's, which could potentially become operational around the same time when F-35 enters large-scale service. Interestingly enough, there has not been "mock dogfights" between combat UAV's and manned aircraft yet, depending on what the results of those would be, the entire F-35 program might be simply too late.