I had neither a Lynx (didn't even know it existed) or a Game Gear when they were new...but I had friends that had Gameboy, which I thought was really cool.
As a collector for Lynx and GG now...I'd say they are both fun to own. Game Gear has such a large library of games. They are a lot that are similar (platform game, fighting games, etc), but the sheer volume of titles and their low prices make it a great system to collect for. The problem is that the caps almost always have to be replaced to get a nice working console.
Lynx is a lot of fun with some really great games and some real duds. The main issue with Lynx is price. A nice working Lynx is hard to find, and games can be costly. Still, it's fun and worthy. But as I said...i didn't know it existed then, and that's a marketing failure. Same for 7800.
Gameboy still remains the king, sorry to say. The consoles were simpler, but they tend to still work great. And so many of them available. And so many great games.