Really? Can you elaborate? Im actually interested. I like parts or characters from them, but not them entirely.
For instance, Green Goblin and JJJamison were top notch. But other things... not so much. Toby made a great Peter, but a bad Spider-man.
Not him, obviously, but I'll step up to the plate and offer my two cents. (Also I started writing, then realized I wrote too much but I can't stop now because I'm too invested).
1) Tone - The most important thing to remember is that Raimi's movies are based almost entirely on 60's-70's Spider-Man. Raimi hits just about the right balance of campiness and dramatic, cycling between the two from scene to scene (at least for the first two). The Amazing Spider-Man is a Spider-Man movie that wishes it was Batman.
2) Direction - The CG hasn't aged all that well, but Raimi's stylistic direction still holds up.
I mean, just take a look at this scene. There's practical effects and stunt work involved here; mix that with Raimi's camerawork and every blow has weight. The audience "feels" every punch Pete takes, which makes the beat down and comeback all the more effective.
Contrast that with, well, this. The camerawork is just kinda... there. There's no real impact when they hit each other, and it just looks like a cartoon or cutscene half of the time. The movie's ten years older but somehow looks far worse.
3) Peter - It seems kinda weird to say, but Peter Park, not Spider-Man, is the core of a Spider-Man movie. Think of it like the Iron Man movies - as cool as the suit may look, if Tony Stark doesn't work, then the movie doesn't work. Toby's Spider-Man was weak, but his Peter was strong, and that's what matters most. Andrew Garfield is just kind of awful as Peter. I don't think it's his fault; the guy's actually a pretty great actor. It's a problem of writing, direction, and casting more than anything else.
4) Writing -
Raimi's Spider-Man has the greatest line of all time. Amazing Spider-Man has Uncle Ben die for chocolate milk. Plus, I don't know, Raimi's stuff is just a lot more memorable and quotable. There's not really any line that sticks out to me from ASM, and making everything tie in to Oscorp is just so damn limiting.
Raimi's movies are far from perfect (MJ's pretty flat as a character, Toby's Spider-Man isn't nearly as quippy as he should be, even I find the corniness a little much at time, Spider-Man 3, etc.), of course. The perfect Spider-Man adaptation was Spectacular Spider-Man, but that was cancelled because we are the playthings of a vengeful, spiteful God.
Raimi's Spider-Man movies are basically the Marvel equivalent of the Donner Superman films. They capture and embrace the Silver Age spirit perfectly - they're cheesy and corny, sure, but endearingly so. The Amazing Spider-Man was just made for the copyright and it shows.
Any disagreements can be filed here.