Well, lets not forget...
The PS1 library had a huge LIST of amazing games. GBA only has about of handful of A+ titles, around 80% of them made by Nintendo. The crap outweighs the good, just run by EB Games or Gamestop and browse through the GBA section.
The PSP is about the size of a Neo-Geo, except much thinner. It's definely more thinner and sleaker than the DS. They're about the same width, but the DS is much thicker due to the folding screen. Not only that, but the PSP screen is huge! I also remember something about it being non-reflection, so there wouldnt be light issues. Either way, the screen is much much bigger than any handheld I've ever seen. The PSP beats DS in the size department either way, pick up any gaming mag that has analyzed the two, and the PSP always has the edge portability wize. Only thing they need is a screen cover really.
I honestly dont see the PS2 being successful just because of backwards compatibility. Not alot of people even use the backwards compatability. Its nice when you first buy it right off and shelf and not alot of games are out, but I dont think thats why people bought it.
By hard cases, do you mean the little shells they put the UMD's in to protect people from copying them? Or the plastic cases that you buy them in? I've seen pictures of them, and they're not as big as the PS2 and Xbox cases, even though they look EXACTLY like them. It kind of threw me off at first, but when you see them put up next to eachother, they're not big at all.
Battery life isnt really an issue for me, because with games its supposed to be 10 hours. GBA SP had a battery life of 10 hours with the backlight on, and I always had the light on, even during the day, it just gives a better screen quality. 10 hours is pretty long really. 8 hours for MP3's isnt too shabby either (Even though Sony just released that 20 gig MP3 player with 30 hours of battery...). The only real flaw the PSP has with battery is movies, 2.5 hours. What happens if you have a 3 hour movie? But they are selling an external battery pack, so if you really need to play games for 11 hours straight...@_@.
The thing that I dont like about the DS is that its release line up isnt that impressing compared to Sony. Sony is doing what it did to the console market, its time to grow up, put down the magical mushrooms and pick up the M4