Spellcasters win, hands down.
Destructive capability: Depending on the level, the destructive capability of well min-maxed fighters or well min-maxed spellcasters should vary. The bonus here is that the spellcasters can generally do their damage from farther away.
party utility: I can't think of one way in which a noncaster is any where near the font of utility that a caster is. A caster can fly, haste, buff, heal, and do any number of special abilities that any of the other classes cannot. The best example here of how casters and noncasters do not match up are in a series of spells that you've seen me use. Teleport, Etherial Jaunt, Etherialness, and Dimension Door are all key abilities that nobody should be able to do without.
problem solving skills: Well, as far as these go, I'd generally say that it depends on the player, not the character. But high mental stats are what the spellcasters are known for, and high mental stats tend to lend better to IC reasons for solving problems.
So all in all, noncasters are useful, but just there to die.