There is, in fact.
Consider a fighter's primary gains: BAB, Hit points, and Feats. These all progress linearly through the levels, so a 10th-level fighter has about double the gains that a 5th-level fighter does. (2 attacks instead of 1, +10 instead of +5, double the hit points, etc.)
Consider a spell-caster's primary gains: More spells, more damage per spell. # of spells doesn't advance linearly, in fact when you see a 'magic-point' style system, to balance with the base wizard, it needs to increase dramatically, a.la 'Elements of Magic's' progression: 2, 3, 5, 9, 14, 22, 30, 40, 52, 66... This is because the core classes progress towards a point where, at 20th level, the caster can cast 4 spells at each level (rather than, say, a pyramid-style where they can cast 8 1st-level spells but only 1 9th-level spell). Using that as an equality-point, we see that the 10th-level wizard is about 4.7 times 'stronger' in terms of number/quality of spells cast compared to a 5th-level wizard. Since the 'damage per spell' has also increased (Fireball is now 10d6 instead of 5d6, for example), the 10th-level wizard has become significantly more powerful compared to a wizard of half his level.
When you draw out an attempt at a 'balance curve' for the classes, you'll wind up finding that the fighter is, in fact, more powerful than the wizard at low levels, and that there is a point where they are near equals, and that there is a point where the wizard has become stronger. Where you declare that point to be depends on your assumptions about how to draw the curve.
Does this mean the game isn't 'balanced'? No, not at all - it means that these two classes are not perfectly balanced against each other at each level; they ARE balanced over the course of an extended-play campaign in which it is reasonable to expect the player who wants to become the world-shaping wizard to slog through some levels of very weak power ("Shoot, I've already cast my one spell for the day!") to 'earn' the right to have the world-shaking power later in the game. There are other balancing factors as well, among them the idea that the fighter can deal his damage all day, while the wizard still has the 'I ran out of spells' problem.
I'm sure a number of people will disagree with that; I'm not trying to start a controversy, merely to offer a possible explanation why the initial poster's group finds the fighter to be so strong, and the arcane classes weak, while other posters observe the opposite: both may be true, depending which level you do the analysis at.