Playing Sonic Rush after having played its sequel (Sonic Rush Adventure) first, it's hard not to compare the two. And in comparison... I'd definitely say Rush Adventure fairs better. That doesn't mean that Rush 1 is a bad game by any means, though. The core appeal of the Rush series is still there (which I'll refrain from covering again here—you can always check out my Rush Adventure review). The game's certainly a lot more to the point, which I appreciate, and it has a lot more stylish flair to it, with the silhouettes as you enter a stage and the colorful aesthetic of the zone intro screen, along with the music. Tomoya Ohtani's work on Rush Adventure is much more what you'd expect from more modern Sonic games (which makes sense, given he's the modern series' composer!), and while that style generally sits with me better, Hideki Naganuma's work here is very distinct. I'd be lying if I claimed not to have A New Day stuck in my head since first playing a special stage. So overall, presentation is great.
The biggest difference you'll notice between Rush and Rush Adventure lies in the level design. Rush 1 is just... well, it's a lot more punishing. Stages are riddled with bottomless pits, and there are plenty of times where your first introduction to a stage gimmick will be in a dangerous area, so you don't have much of any time to figure out how it works before you're thrust into a life or death situation with it. Past the first two zones, I found myself getting a game over on every single stage at least once before making it through (I think my record was three game overs before making it through). It's a tough game! Or maybe I'm not super good (I have a tendency to panic jump, and when jumping dismounts you from most stage gimmicks and there's usually bottomless pits underneath... it's not a good combo). It certainly makes it feel so much more rewarding when you finally make it through, but the flip side is that it feels unfair most of the time. The most enjoyable point of the game because of this is Blaze's playthrough, where you've likely already beaten the game as Sonic and already know what to look out for in each stage more. As evident, I didn't get a single game over as Blaze and beat the game in an hour less because of it. Plus, her midair upwards dash thing launches you so much farther upwards and'll save your skin a lot compared to the puny vertical distance Sonic gets out of the move (funny how I never noticed how big the difference was until now because I practically never played as Sonic in Rush Adventure...).
Other big difference gameplay wise? The bosses SUCK. Oh my god, they're all so tedious and make you want to rip your hair out. Ugh. Literally all just the formula of sitting around dodging attacks until an opportunity opens for you to attack them yourself. It's not very fun.
As for the story, it's communicated pretty poorly and generally doesn't make a whole lot of sense? Like, Blaze is from some sort of parallel universe, along with Eggman Nega (who's her version of Eggman, if you couldn't guess), and she somehow got transported to Sonic's world thanks to something one of the Eggmen did with either the Chaos Emeralds or the Sol Emeralds. The details are pretty vague, and the manual doesn't even help (it's literally like one page telling you the most basic controls... how disappointing!). But Sonic fights Eggman Nega to try and figure out what's going on, while Blaze (who somehow knows exactly what's going on) fights normal Eggman to get the Sol Emeralds back so she can use them to go home. But there are continuity errors between Sonic and Blaze's story, since both fight the same bosses, but piloted by the opposite Eggman (and the climaxes don't quite match up either), so the whole thing just feels very rushed, like there wasn't time to think things through all the way. And the dialogue all feels so corny and unnatural, which very well could be a localization thing (I'm not convinced that the translation team was given as much time or money as they needed), though I do appreciate the whole story of Blaze learning to open up and be able to rely on others. I think it'd hit harder if it wasn't so on the nose though.
In some ways, playing Sonic Rush makes me appreciate more just how effective of a sequel Rush Adventure was, refining so much of Rush's core gameplay while adding on better writing and side content. At the same time though, I can see some of Rush 1's merits. It's trimmed a lot of the fat (or rather... was just made before the fat was gained in the first place), and has a distinct style to it. It feels a lot more satisfying to beat because of how much tougher it is, though the way that manifests is unfortunately through level design that feels unfair. Perhaps if the Rush series got another shot, it could've found a way to combine the best of both worlds.