I just bought a DS Lite used (barely!) off of someone I know for an excellent deal... otherwise I might never have bought one... and I LOVE it! With the huge selection of games for the GBA compatible with the DS, as well as a nice library of games for the DS... I've been playing it almost daily since I bought it!
I've been playing Castlevania: Dawn of Sorrow and Advance Wars: Dual Strike and while they don't make a lot of use of the touch screen, the little added features are nice and they really make a great use of the two screen setup! In the GBA prequels, you had to press a button to bring up the maps/status screens but now you don't because of the additional screen real estate. PSP uses look down on this feature as "fluff" but it really does make the gameplay experience more streamlined.
And Elite Beat Agents is one of those really strange music games that happens to be a lot of fun, making full use of the touch screen (you never touch a single button while playing this game). Then there's also Trauma Center, surprisingly fun, and Pokemon DP, which you may or may not be interested in. I've only spent a few hours in Pokemon DP but I can say it is definitely an improvement over the older games, with Wi-Fi support for battling and trading other gamers locally and worldwide, and VoIP support so you can smack talk your friends.
I do have a PSP and while it is a lot of fun... I think the DS is a clear winner if you are looking for pure gaming fun. The PSP does offer some great multimedia options so if you are looking for a portable entertainment center, it is the way to go. Between Grand Theft Auto * Stories, Metal Gear Solid Portable Ops, Killzone, Virtua Tennis, Burnout Legends, Daxter, etc, you can get your fill of console gaming on the go... with some truly high-quality titles, not to mention very portable-friendly games like LocoRoco and Lumines.
IHA, I'd disagree with you on that. The PSP is a great system, but the NDS is an incredibly underrated portable whose AAA titles cannot be ignored. I see the NDS and PSP filling different niches, with the PSP offering console gaming on the go, and the NDS offering a truly refreshing experience where old-school games are modernized, like the truly classic Castlevania series that made a very poor jump to 3D. I'm a big fan of both systems as they both have some great games, but if I had to pick one, the NDS would be my top choice. It's just more FUN.
Edit: Another thought, phone games really are terrible, perhaps with few exceptions. I have Brothers in Arms 3D, Splinter Cell Double Agent, and Time Crisis Mobile. While the 3D graphics are pretty good, especially coming from a phone, and the games are actually somewhat fun, the limitations of the cellphone hardware really makes control an issue. Maybe if you only play puzzle games like Lumines Mobile (which I have had), Tetris and Bejeweled... Probably why the N-Gage failed so badly.