I think that the answer ought to be: he doesn't (compete, that is).
I think it's fine for some classes to be unable to compete with others in certain spheres, at certain times, or in certain circumstances. A fighter (of just about any level) unable to compete with a high-level wizard seems pretty logical to me. I've never felt compelled to play a wizard (or a spellcaster) over any other class in 1E and 3E, because the other classes were still fun to play.
I also think that the basic precept that classes ought to be balanced is flawed. A RPG is not about competition anyway. If it was, the DM could simply have all PCs die and be done with it, and he'd win. An RPG is about an experience in gaming where character flaws
contribute to the story. This is recognized by many, some gaming systems even include flaws in the core rules (Savage Worlds, for example). If I play a fighter that wishes to defeat a wizard, the idea is not to find a way to slay the invisible, flying, protected-from-arrows mage in a 1v1 battle; it's about finding a way to defeat him when he's not invisible, flying and protected from arrows.
So I think that a wizard outshining a fighter in high-level combat should be expected. The fighter still needs to be in that adventure group when the wizard hasn't cast his protective spells, when the group is low level, and generally he's always pretty useful anyway, in the end. (And many fighters find a way to fly too, ultimately

).