Atacks on par? A level 9 fighter hits AC 0 on a 12 sans bonus. A level 9 cleric hits AC 0 on a 16. Sure we could assume the cleric has magic items to make this up that the fighter for some reason doesn't have access to but the cleric is still behind the fighter on the combat tables everything else being equal.
High level casters are very powerful but not without limitations. A level 9 magic user has 4 1st, 3 2nd, 3 3rd, 2 4th, and 1 5th level spell per day. These need to be carefully chosen to balance offensive, defensive, and misc. needs. If the MU decides to allot all spells to doing one thing for the day then he/she will be very weak in other areas.
Want to use charm to avoid negotiating with that NPC? Go for it but its a resource you won't have later.
Also certain magic items cannot be assumed to be freely available just because a character is at level X or has a certain amount of gold. Spells are also much easier to disrupt since a caster must declare them prior to initiative, cannot move, or even use a DEX bonus to boost his/her pitiful AC.
Oh but the caster has shield, protection from normal missiles, mirror image, etc.
Well yes, but these take valuable spell slots and don't last forever. If the rules are actually used then casters are not the unstoppable monstrocities that they are made out to be.
The Fighter has also got his 1/2 extra attack, by 9th level. At lower levels they aren't as far ahead of the cleric, but certainly in AD&D/BD&D the Fighter is much better than the Cleric at combat. I have things I don't like about the Fighter in those games, but that is not one of them.
On the other hand, that isn't remotely as true of 3rd edition. A lot of people don't want it to be true of 5th. I have some hope that Mearls is enough of an AD&D fan to make sure this happens, but there are also people extremely insistent that a game that isn't like 3e won't satisfy them, and this is supposed to be the one edition to unify them all. And we've already seen signs, in the cleric article, that gaining abilities similar to those of a ranger will be perfectly practical for a cleric of Apollo (who should be a cleric of Artemis, of course) and unless they're going to be bad at those things, then they're going to have to give up an awful lot of cleric-stuff to not end up being strictly better than the ranger.
Whether it's a good thing to have more than one way to make a character concept is a separate question. But if you allow someone to make a character concept one way, and then you give them another way to make that concept which also gives them other things on top, that's going to lead to some interesting results.