I've been banking with Navy Fed for 17 years, and have had insurance with USAA for 20+ years.
Banking: Both USAA and Navy Fed have competitive interest rates, and both banks are very user friendly. For those sea service folks who are looking at doing some overseas stuff, Navy Fed does have branches at most major naval bases overseas, and being able to talk with someone face to face can be a life saver at times. USAA does refund your ATM fees where Navy Fed does not. If your use a Star ATM there are no fees, and one little secret with Navy Fed, most (not all) 7-11 ATM's are fee free.
For deposits, USAA has a program where you can scan a check and import the image into USAA's online banking web page, and the check will be deposited to the account within 24 hours.
I've looked at both banks pretty closely, and for now Navy Fed has what I need. Personal choice, but make sure to look at all the rates first.
Insurance: USAA can't be beat IMHO. The rates are good for auto and have been great for homeowners. The claims folks are outstanding, not that anyone should ever have to use them, but if you do they are on the ball and really make what is a bad situation that much easier.