My character had both. I could cast 9th level spells. I had the same DCs on my spells as did the wizard in our group. Due to my spells, I had the same(or within 1) attack bonus as the fighter in our group. I had the same number of attacks, since I had a 17 BAB.
But, especially at high levels in 3e, monsters are engineered in a very binary fashion. The whole "fighter can't be hit, the rogue can't be missed" issue. Three points of BAB means missing in one round that your entire party is hit with a
wail of the banshee. Three points of caster level when going up against things with insane SR means you're a pussycat. MAD sapping your saving throw DC's means that even if you hit, the critter shrugs it off.
Against a whole party where, as a group, they have full everything, the binary monsters are an "appropriate challenge" (ish).
Against someone who is three points behind in everything, the binary monsters crush you.
You can do as much as anyone else on paper, but that slight lag in stats is VERY significant when hitting that upper echelon of monsters, who are designed to be very difficult to people with significantly better ability.
I mean, a monk's
flurry of whiffs is only -2. No one ever hits with their second or third or fourth (ha!) attacks. Just because you're a one-man party doesn't mean you can take on the enemies that a party could take on.
Sixteen attacks at -5 is not the same as one attack at +5, especially when, in order to hit the thing, you need an 18 or better even at +5.
But it was possible using all the published books to find a bonus with almost every feat if you looked hard enough.
At that point, you're just making up for lost time, though. The monsters assume that the pure fighter took those same feats, so their AC is still all that much harder for you to hit.
My general rule is that if your highest level spell is more than 1 level below a wizard of your level or you get more than 3 BAB away from a fighter of your level, then you are disadvantaged in either spellcasting or fighting. (Which, of course, means that you shouldn't be fighting in melee with a single classed Rogue at 20th level, BTW) If you remain with those guidelines, you are still a legitimate melee character or caster.
The anecdotal evidence there is a bit fiddly, because there's a lot of variables aside from your character that aren't really accounted for. There are campaigns where a straight cleric will be grossly overpowered compared to the rest of the party. I'm not sure I'd use that as a place to launch my "clerics are overpowered" speech.
Because it was much easier to create a sucky character than it was a good one using multiclassing. But it was certainly possible to use certain multiclasses to be better than a single class character.
The trade-offs weren't always equal, right. And we agree on the first point -- the bigger multiclassing risk was to make a character that wasn't very effective at the things he was supposed to be doing. Someone with a good head for numbers probably could squeak out the system while limiting the things he gave up, especially once they could consider the campaign, the other party members, the monster tastes of the DM, and other things.
Though I think the broader message of this convo is that 3e had a mess of issues with multiclassing that 4e is trying to solve, and that you aren't likely to see the return of old-school multiclassing (in a 3e or 2e or 1e sense) any time soon.
Which raises the question of what, exactly, dual-classing will do.