I just purchased a new LTE AT&T iPad 3. I am a current iPhone 4 user with AT&T. I would like to be able to use my iPad 3 occasionally for data access by just moving my iPhone SIM to the iPad. I have done this previously with my 3G iPad and it worked perfectly.

I tried doing this on my new iPad but got an error on the iPad that this wasn't an LTE SIM. So I'm wondering if I can just get an LTE SIM card for my iPhone and swap that back and forth. I know I wouldn't have LTE when I use the iPhone, but would I get LTE speed on the iPad and then would the phone continue to work on 3G? Would I just need to get an LTE capable SIM card to replace my current iPhone 3G card?

Any reason that this wouldn't work?