Is there one router that works better with iPhone than another?

The ones with better range and speed.

I would recommend the Apple Airport Base Station. It uses the fastest widely available protocol (802.11e) and of course works seamlessly with iPhone. If you have a Mac with 802.11e, you will see a huge speed and range increase in your home network.

No.

my Apple AirPort Extreme gives me better signal and speed than the LinkSys at work... And I'm physically closer to the LinkSys and my desktop is the only other device using it (there are a total of 4 PCs on the network, but the others are hard-wired).

At home I have 2 iMacs and 2 iPhones on the AirPort wireless and 1 PC wired in to our cable modem. The new AirPort Extreme is EVEN FASTER... I'll probably get it when Leopard comes put in the fall.