I had a Lynx and I wasn't that impressed with it. It had advanced graphics for the time, even with SNES's scaling/rotation and on sprites too boot (with projection as a catered to feature) but it was crippled by the tiny resolution (even smaller than Gameboy's!) and lack of colors (only 16 on-screen, worse than say, the 32 Game Gear offered)
Sure, it was backlit (backlighting/screen weren't very great) and had color, which was more than could be said for Gameboy, but what it offered didn't make it worth the battery guzzling.
I think my biggest pet peeve was how little effort developers (for the games I played anyway) put into sound. But that's what happens when you just give developers some DACs and tell them to go nuts, especially if you don't give them a coprocessor for it. Sure, you could do all kinds of cool things with this in theory, but Lynx didn't have the CPU to easily generate waveforms very well, so what you ended up with was a bunch of games that didn't even have music at all. I was pretty disappointed when I got Toki and found it dropped the music found in the NES version - some use of that "32-bit" sound. Gameboy games made much better use of its PSG.