Verizon Blackberry
Verizon DOES work internationally. In fact the coverage is better than ATT as it works in Korea and ATT doesn't. Otherwise the Verizon and ATT coverage are identical on the international map. You need to get the 8830 world phone (blackberry) or the Storm. Then make sure it is internationally enabled (meaning the put the chip in it). I have had my 8830 for two years without a problem and I am in China, Dubai, EU, Korea, etc, etc, etc.
ATT customer service sucks as much as Verizon, so there is no difference there. Don’t know much about T mobile, but Sprint is useless.
If you want a touch phone, go with the Verizon Storm. If you send lots of email from your phone then get the 8830 world phone as the actual keyboard is better than the touch screen.