I have U-Verse ....
... and I can tell you a few things.
1. No, the U-Verse "RG-1000 residential gateway" (their router) does not really have a stronger wi-fi signal than any other comparable wireless router. It's not using anything special, hardware-wise, inside. It's your typical 802.11g wi-fi and nothing more. It doesn't even have an external antenna on it, meaning it's probably WORSE than some models.
2. There's a long-standing firmware bug in the U-Verse gateway that will cause it to suddenly stop issuing out IP addresses via DHCP to wireless devices, if you've got too many different wireless devices on your home network. I'm not exactly sure what the limit is, but the problem started appearing on about a "once every 1-3 days" basis for me when the kids got iPod touches and we linked them up to the wi-fi. Before that, I probably had about 4 wireless devices linked up and working normally.
3. I recommend what someone else suggested; disabling the wireless radio in the U-Verse gateway (easy to do from a web browser) and attaching something like like an Airport Extreme to one of the wired ports on the back of it. Use it to make all your wireless connections. You'll be upgrading to wireless "n" and bypass the firmware flaw, plus likely get a little better signal strength too.