Yeah, Ace Combat 04 is like Ace Combat 2 done right--good, non-repetitive missions with a story that doesn't let it detract from the gameplay.
The problem with Ace Combat 3 is that it gets a bit too deep into the story, enough to make the missions follow the story as opposed to the other way around. For example, the... 3rd? 4th? mission of the game has you following around General Resource's ace Abyssal Dision and his wingman Keith Bryan. Dision and Keith tell you to keep up for about a minute and then you shoot down some targets with your gun. It's a way to introduce you to Dision and Keith, but it's kind of forced. Plus, the guy flies like some of the more insane pilots in Ace Combat 5.
Then they shoehorn in some airdropped chemicals from Neucom that you need to shoot down with your gun. Yeah, the entire missions, as it turns out, was a tutorial mission to tell you how to shoot your gun. I'm playing on hard, I don't need to know that! (Hard was the hardest difficulty in AC3)
EDIT: If there's one thing I really think that they did better in later Ace Combat games, it's the music. AC3's music is generic electronic stuff, very Ridge Racer (which makes sense, since the Ridge Racer series has made more reference to Ace Combat 3 than the Ace Combat series has...).
Also, the remake of Ace Combat 2 on the 3DS has got me excited for the possibility of further remakes.