I second that Wunderground's mobile site (m.wund.com) is far more accurate, at least in LA. I just deleted WeatherEye after a month of use. It is constantly displaying temparatures 10 degrees cooler than reality. Wunderground breaks it down by zip code - not just city - so if you live in a metropolis like LA where the temp changes a lot depending on where you are, you need a more sophisticated site like wunderground.
I've been a severe weather spotter for 14 years and a good, fast loading radar image can be very useful.
I have been using Accuweather and my local NOAA sites to suit my needs.
Ever use WeatherTap.com? I subscribed to their web site for home/desktop use well before I got a BB - and found they have a mobile site that is a part of the subscription - best radar out there.
I also use a program running on my desktop called InterWarn that feeds warnings via email straight to my BB. I get those at the same time the NOAA wx radio goes off, and before the local media air the warnings.