I would transfer the balance to another card if the APR was better on the other card, that is just common sense, you are paying less interest that way!
If you transfer your balance from one first credit card to your 2nd credit card, what will happen to your first card? Are your required to close your first card?
I don't think you are require to close your credit card at all, as you can keep using it, but what's the point? You wanted to close it, so I would just close it!
Transferring balances to lower interest rates can really save money. However, if you happen to charge your card which once held the initial balance it does little good and lots of harm.