There's just too many posts for me to read. So I'll just go off of the first 5 pages I've read.
Some people prefer Verizon (my sister has it with her BB Storm) some prefer AT&T (I have iPhone). Both actually work in Mexico, believe it or not, while my younger brother has T-Mobile with his G1 which doesn't work in Mexico. Anyway, this is irrelevant, but to an extent as it defines service a little.
If these two products come out for Verizon, particularly the iPhone lite, two things must be taken into consideration:
1. Has to be available for AT&T as well. As someone else has mentioned, if it's only available for Verizon. Why would a carrier want to LOSE a customer, lose money. Of course you can have two carriers, but why would you WANT two carriers?
2. This is on Apple's side; If they're going to make this Lite work, there has to be features that differentiate it from the main iPhone. As someone mentioned again, people might just save a couple of more dollars and just get the higher-end one. Of course this might be a little contradicting since it would be the same case as the Touch and the iPhone, one has less features. But at the end of the day, both will be phones. It seems to me the "lite" is price and less features.
As far as carriers go, I'm happy with AT&T. People have been talking about cocky-ness. If you ask me, Verizon is the cocky one, imo. Any carrier that offers any Apple product deserves to be cocky. 😉