The F-35A has better instantaneous and sustained turn rates than an F-16 carrying a war load. A clean F-16 in "air show mode" has a maximum sustained turn rate of 18 degrees per second. The F-35A carrying an A2A war load and full fuel has a sustained turn rate of 17 degrees per second. The F-35 has better acceleration and top speed than the F-16 carrying a war load, and that's with the F-35 carrying 3.5 times more internal fuel than the F-16. The F-16 is actually structurally limited to 4G's if carrying external fuel or bombs.
Having been through this before, this is an interesting and
often overlooked aspect. It's true that you usually hear numbers that sound fabulous but don't relate to the real world and this can make comparison difficult. For instance, when comparing the F-14D and F-18C, the F-18C outturns the F-14; however, this is slick, with no external stores and, in the case of the Hornet, the performance quoted are numbers obtained with its wing pylons removed. Of course, the F-14 is much faster but it's easily outturned (if you fight the Hornet's fight but that's a different subject). Of course neither airplane is of much use without weapons and fuel so what about what we call the "fleet" configuration? How these planes will be loaded in the real world. The Tomcat adds two relatively small external fuel tanks directly under the nacelles while the Hornet adds two, or even three relatively enormous external tanks with large pylons. In this combat configuration the playing field is really leveled. Even if both get rid of their external tanks the Hornet cannot dump it's pylons so is always compromised while the Tomcat, whose tank stub pylons aren't even noticable, is much cleaner. The biggest difference then becomes the flying qualities and the Hornet wins this due to it's fly-by-wire design.
These exact same questions are relevant now. I don't know where you got these numbers but, if true, it sure seems that with equal loadouts the F-35 should out perform the F-16, especially given that it's weapons are internal rather than hanging out creating drag. Also, there is the subjective issue of flying quality which can be very underrated. From what I've heard the airplane is extremely easy to handle but I'm not sure how you could improve on the F-16's flying qualities which are also supurb and I don't know how easy the newer generations of potential adversaries handle. I hear they're pretty good also so I have no idea how they would stack up. Then there's another, somewhat philisophical question. Do you make the plane turn or do you make the missiles turn? Here would be an extreme example. Suppose you had a stealth aircraft that couldn't turn real well but equip it with missiles that can be fired against targets anywhere in the vicinity (using the helmet mounted sight for instance) while the adversaries all have to pretty much turn their planes to launch their missiles at you. Who's better off? What if you can see a guy swinging your wingline for a rear quarter attack on you but, instead of just being able to see him you can launch a missile at him without ever having to turn or slow down? Every time you think about going faster or turning tighter you put the technology into a missile and sling it on the same plane rather than redesign the plane for improved performance. Kinda makes you think, doesn't it? BTW, where did you get the performance numbers if you don't mind me asking?
The F-35 can carry the AIM-9X Sidewinder and IRIS-T dogfight missiles. And, as you point out, it has a gun. This is one issue where Wheeler really shows how delusional he is, or more likely deliberately untruthful. The whole point of developing that fancy helmet is to guide those dogfight missiles.
I disregarded Wheeler when I watched one of the videos posted (the Australian one I believe). Where he lost me is when he complained about the F-35's heavy computerization and how if the computers crashed the F-35 would just fall out of the sky. I seem to recall a whole bunch of similar complaints about another new airplane. What was that plane....OH, I remember, it was the F-16 which was the first totally fly-by-wire fighter in the world and, relatively speaking, was as heavily computerized for its time as the F-35 is for its. The F-16 has no backups to the FBW, if the computers crash it'll crash. WTH is this guy doing making such an argument?