It depends really. The downsides are that the battery life is somewhat shorter, even on the lowest light setting I always use and it can't play GBA games, but I assume you know both of those things. I only ever notice the screen difference when I go from one device to the other.|
Other than that though, it's very nice. The sound production it uses (I almost always use headphones) is noticeably crisper and louder at first, but as sound goes, you eventually don't notice it any more. So I can't say any old games that I'm playing, I'm noticing any new subtleties in the music and sound effects at this point.
DSiWare is the biggest reason you'd want one and it looks pretty good at this point - the first third party games are coming out now and Nintendo has been supporting DSiWare with a lot more content themselves than they have Wiiware. One thing I like is that some of the games are for it are smaller, more focused versions of other DS games -- so you can get an extension of a game you liked or if you're not sure you want a game, a piece of it for very very little money. I've found with two games now that I'm happy with the piece I've got and don't want the full version, so that's extremely helpful. The ability to play lots of different games without switching out any cartridges is of course, fantastic on the go.
Lots of the ArtStyle games Nintendo releases for it are terribly unique puzzler experiments that get addictive.
But the best thing is the Moving Memo application you can download for free. Ever since it came out it has been a constant source of glee. It's almost like the Mario Paint followup I've always wanted. Doodling a bit in my spare time is so easy (as is uploading the finished movie) and I check the site that collects all the movies (which is fiendishly popular) as much or more than the big movie sites like Nico Nico or Youtube. Some of the multi-part storylines users make that continue for days and weeks there are really inventive.
I usually take my iPod and my DS around with me, so with the DSi able to play MP3s now, it's done conveniently enough that sometimes I can just take my DSi and go with that. That it has to share its function with other things and is not as small or convenient is against it, but it helps reduce portable glut too. Like when I get new music and all I want to do is listen to it on the train, I can just put it on my DSi. When I want a much larger selection or don't want to have the DSi in my pocket, I bring along my iPod. It's nice to be able to switch between the two, because the PSP's form factor makes it way too hard to be as convenient.
Myself, I like to play around like gadgets like the camera from time to time, even on my cellphone, so the DSi camera with all its quirks -- well, sometimes I get the urge to try something out. It's also been helpful for all the reasons a cellphone camera usually is when I don't have my cellphone -- you know, the type of thing where you're at a bookstore and you see an enticing new author you know you won't remember the name for, but you don't want to buy right now, so you take a picture to remind yourself.
That's what it's like for me, owning a DSi, your mileage may vary. Overall, I find DSiware the biggest advantage, and I like that it helps me simplify my need to carry around portable gadgets from time to time. I still keep my Lite around for GBA games and it can be useful to switch between them also when you want to keep playing away from an outlet but you don't want to charge one or the other.