Another post on the top ten troll questions.
(7). Are magic-users more powerful than fighters (and, if yes, what level do they take the lead)?
Well, no, they aren't more powerful than fighters. They can do something fighters normally can't do, but basically, only once, maybe up to four times.
The thing about the fighter/magic-user comparisons is that they always use unique situations as if they were common occurrences. "A 5th level Magic-User could cast a fireball that does five dice of damage, but a Fighter can only do a single die of damage." Well, yeah, a Magic-Usercould do that. Once. If it's a known spell. And if the casting isn't interrupted. Magic-Users aren't universally competent; they just have access to unusual tools.
The way to look at it is: Fighters are people who rely completely on ordinary might and whatever tools they can find, magical or otherwise, while other classes sacrifice general improvement of hit dice and combat ability for limited exceptional abilities. A Fighter can fight all day. A 1st level Fighter with a flaming sword can do much more damage over time than a 5th level Magic-User. A 5th level Fighter with a flaming sword facing five 1 hit die zombies can wipe them out in a single round -- and still has a flaming sword when the round is over.
Choosing a class is not about "Which class is more powerful?" but "Which options do I want to pursue later?"