While ads are often full of hyperbole and Atari was later known for some sketchy match (the "64-bit" Atari Jaguar), I think the Atari Lynx really was vastly superior to the competition. Released only 2 months after the Game Boy, it had a 16-bit processor and full color screen. And, unlike most Atari systems after the 2600 it actually a reasonable quantity of reasonable quality games.
The other portables the Lynx competed with included of course the Game Boy, as well as the Turbo Express and Sega Game Gear. Ultimately the Game Boy won out largely because of their price, large game library (partially due to their draconian licensing policies) and battery life. The Turbo Express was a nice system but it was very expensive and games originally designed for a big screen didn't always work as well on a small screen. The Game Gear came along a little later and was based on the Master System hardware. To me, the real color portable competition was between the Game Gear and Lynx but both ultimately lost out to the Game Boy.
One of the reasons the Lynx had a decent games library was due to the fact that it was developed by Epyx, a company known largely for their 8-bit computer games. If it had been Atari alone doing this then I'm quite sure the Lynx would have been far less successful. Despite the Lynx's relatively low sales (at least when compared to the Game Boy) it was still a success for Atari. It sold well for a while and made Atari money. There was even a cost reduced hardware redesign that was smaller and lighter that was released in 1991. And to be fair, the consoles were sold all the way through 1995 with Atari releasing games through about 1996. Telegames continued releasing games throughout the 1990s.
The Lynx was my favorite portable from that era. I'm spoiled by today's small screen quality so I don't think any of those portables holds up well today if you are playing on an original system with original screen. Too much motion blur and the colors are too washed out looking. But check out an emulator to see what the games were like. Some were quite fun.
