Note: i live in europe, have no experience w. american banks.
Whenever i've had pain with my banks, it's always been revolving around exceptions, and not everyday business like paying the bills. Examples of 'pain with the bank' for me has been malfunctioning cards, accounts that are not hooked up to online banking, the bank having the wrong address for me, etc. Essentially: problems that currently can't be solved online with the mainstream banks.
It's gonna be very interesting to see if banksimple/simple can do something about making these things easir to deal with.