I highly recommend switching to USAA for a checking account. Their customer service is excellent, they are experienced with military matters (preparing for a deployment was a single phone call), they allow mobile check deposits, and their insurance rates were far cheaper than anywhere else that we could find.
However, we keep our emergency fund at Ally. The number 1 reason was to get the higher interest rate (almost 3 times higher than USAA). After moving our emergency fund to Ally, we also appreciated having the physical separation between the accounts. We have dipped into our emergency fund once or twice, and the easiest way we found to transfer money was to write a check out of Ally and deposit it with USAA's mobile depositing; the whole process took about two minutes.
"Successful investing is all about common sense." | ~ John Bogle.