Long-ass first post ahead!
The Advance games are a curious thing for me, because I first played parts 1 and 2 on Visual Boy back when they were released. I didn't even have a GBA myself back then, but part 1 seemed pretty boring to me, and party 2 frustrated me because I kept falling into the very same bottomless pit over and over (this was in world 4).
Fast forward a couple of years, and I got myself a cheap GBA SP and am hunting down cheap games at Gamestop and see the Sonic Advance / Sonic Battle package for 5 €uros. Since I actually had good memories of Sonic Battle and felt like playing some 2D Sonic again, I figured, eh, what the hell. Advance 1, however, still seemed kind of lifeless - it was a nice enough game, but it wasn't quite as fast paced as I'd expected - which is funny, because I guess I'm in the minority, but I think Sonic 1 (Genesis) can easily stand up to its to sequels. I have no problem with slower gameplay and a lack of BLAST PROCESSING; it's just the levels felt a bit bland or lacking in terms of actual events. However, after having spent some time also playing the sequels (I won't go into detail about in which order I got them, enough of the storytelling already), especially Advance 3, I definitely learned to appreciate Advance 1's tight controls and well-arranged layout.
So, Advance 1: It definitely could be a bit more exciting - not in terms of speed or anything, but in terms of level design, which often seems kind of safe and predictable. Also, the various routes are not quite as elegantly laid out as in the old games. You don't make a certain jump, you're condemned to take the lower route - it's nice to have a lower route, but still it feels a bit clumsy at times, and as a result I'm often somewhat indifferent to which route I end up on, since there's not a whole lot going on on either one anyway.
The control is great, though, and there's very few frustrating / unfair parts. The game is very short, though, and the polish is a bit lacking - an overworld map would've required not much effort but at least given some sort of continuity to the levels. In my personal hierarchy of the Advance titles, it comes in at #2. The graphics are not bad but not stunning, and most of the zones do feel like rehashes. I like the music, though it's not quite as catchy as I'd hoped. I never even completed a single special stage, so I never saw the "real" ending. I definitely like Advance 3's more and have never even seen 2's. It's actually hard to explain what's wrong with the game other than it's just a bit on the bland side design-wise.
Also, not really the games' fault, but I'd prefer the camera to be a bit more distant, but I won't blame Dimps for the GBA's limited resolution.
Advance 2 is probably my PERSONAL favorite of the 3 Advance games, but it's not the best designed game. I enjoy speedrunning some of the levels, and that is what I also feel that the game was designed for, considering its gameplay certainly emphasizes the speed. At first, it was my least favorite of the games, for the same reason - playing the game for the first time is a bitch, because it does require memorization at times, and that sucks in any platformer. But when it does not, or if you have a level that requires it memorized, it's just great fun to breeze through the stages. The later stages are a total bitch, though (I only ever completed the game with Cream) and some of the enemy placement is downright horrible - I've been launched into enemies by springs more than once, and in one case, I actually saw the enemy approaching, quickly tried to attack him with the trick button, only to have fucking spikes rush out of the ground (the gravity was reversed when this happened) while Sonic was charging his spin attack and hurt me. I was literally unable to escape the situation just by reaction, and you could not see the enemy (or spikes) beforehand. Also, the homing attack is a pretty useless addition, especially since if you try to use Sonic's normal kick (which he still has) close to a spikey guy, of course Sonic won't just kick through the spikes but home in on the enemy and proceed to suffer damage... Either give the homing attack its own button or ditch one of the two, but this way it's just stupid.
So why do I like the game? First of all, I like the overall atmosphere. Leaf Forest is a great zone, as is Ice Paradise (I wish the background was animated, though; it basically screams for it). The addition of a overworld map is also a nice touch. But above all, the replay value of the levels that do not suck is immense. I spent quite a lot of time speedrunning Leaf Forest Act 1 (my record is 49.55 I think - definitely 49, not sure about the miliseconds), but when I saw a Youtube video speedrunning it, the guy took a completely different route and even fucked up in a couple of spots and still was barely slower. So there's lots of room for personal improvement and finetuning, which is what makes it a great game for speedrunning. Also, although I hated the level at first, Ice Paradise is a great zone. Lots of stuff going on here, lots of alternative routes that actually play different, and plenty of fast paced sequences that still can be done without clarvoiance or memorization. If I just were to play through a game from beginning to, end, though, this would most likely not be my choice, if only for the fucking Bitchslap of Doom courtesy of Knuckles. Seriously, I have no problem with the Zone itself, but the boss is just annoying beyond belief. Of course, with Cream, he's easy, but she's practically overpowered. I also never ever even entered a special stage, but unlike with SA1 or SA3, I don't even plan on collecting all the emeralds in, like, ever, especially since - as far as I know - you need to get 'em with EVERY character to get the true final boss and Amy. That's just too much work and not enough fun for me.
Advance 3 was my favorite at first, and I still can see why: It does a lot of things I wished the other two titles had done - it has an overworld (sorry, I like that), its longer than any of the previous titles, a lot of the zones are pretty original, and the partner-system seemed pretty cool. However, the execution is lacking.
For one, like I mentioned before, the controls are incredibly slippery compared to Advance 1. Advance 2 put more emphasis on speed, and increased the overall tempo, but it was playable because there was very little tricky platforming. Advance 3 has slippery controls and tons of platforming, resulting in very hectic parts. Plus the pacing sucks - in Sunset Hill, there's a part where you run down a slope, killing enemies and running on water along the way, and immediately thereafter are platforms... with a bottomless pit below. I think I burned at leat 5 lives on that part, because the change is not even indicated at all - one part is totally tailored for you to run like crazy, and then there's a part which required to stand still, wait for platforms to scroll in and carefully jump onto them... with the platforms not even being on screen at first, my first reaction was to just jump and head for below - only to find out it's a friggin bottomless pit. The game is just sending wrong signals all the way here.
The whole "running up walls and on the ceiling"-thing also backfires frequently with its poor control (hold right to run left and not fall down?), and often enough, enemies are put in such sections, or better yet, spikes emerging from the floor... the later being a general evil with the GBA titles. But what really bothers me is the fact that the levels often feel cluttered. Despite some nice graphics, I can hardly even tell if I've been in a section before or not, because it all seems very same. Some said they were trying to replicate the bigger environments of 3K - that's a nice idea, but often the levels just feel confusing since it all blends together. Ocean Base is especially guilty of this. Also, I just don't like some of the designs - the basic approaches often were pretty great (Route 99 is a great level in concept), but the final product just seems lacking. Ocean Base again is a pretty cool idea and I actually like the darker angle, but it's often just confusing and overloaded. Also, the music sucks at times - the overworld theme is especially weird at times, and unless I'm mistaken, there's actually a couple of sour notes in Sunset Hill which is pretty much sacrilege.
But despite some truly shitty level design (Route 99 is especially guilty of this, which is a double-shame since it's the first zone and thus should start the game with a good impression), there is some fun to be had here. I actually like the partner system, and I liked the boss battles more than 2's which wore off their "you're running all the time!"-novelty very soon. Again, the ice stage (Twinkle Snow) is fun to play and also features a handful of gimmicks (running on water AND carts AND those rings shooting you around). The special stages are fun, and the way to enter them is, well, not a bad idea actually. I don't love the game enough to search all the Chaos on my own, but it certainly gives the game a nice replay value. The bonus games on the overworld are also a nice touch, as are the hidden Chaos in the overworlds themselves. The stages that have discernable multiple routes are also a lot of fun for that reason - the levels actually feel huge then (they don't if you're not sure if you've seen it before anyway). Minor nitpick would be that it's often unclear which route is supposed to be hidden / harder to access and you accidently take a route that was supposed to be the one obvious and thus contains less extra stuff in its way.
In general, this game showed a lot of promise, and suffers from a somewhat flawed execution. None of the Advance games were extremely polished, but this one certainly showed it the most, if only for the fact that it also contained the most stuff and thus would've probably needed more extensive testing and finetuning.
Overall order of the Advance-games, from favorite to least favorite: 2 > 1 > 3. They're all worth a shot, though, since they're actually pretty different from another and all have their strengths and weaknesses.
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And the special stage entry was almost as bad as Advance 2's, but more worth it for the awesome Special Stages and great final boss. Which I won't spoil for you. Anyway the only level that really gave me hell was Cosmic Angel Act 3. You know the part, with those fucking falling boulders and that tiny ass platform you had to stand on for like five minutes at a time and uuurggghh. But yeah, overall, a nice game, and not a bad way to cap off the series. Also dose Green Hill Zone remixes. 
