Bank?, Good Service?, not possible!
Most expats go for HSBC because of the name, but as chocs said, the name counts for SFA when you put dickheads in charge of it locally.
Although I can't complain too much and have had a good run with Emirates NBD, Mashalah. Only had a problem trying to bring money into the UAE as it tends to disappear into cyberspace until you ring someone and ask them to empty their inbox.
If the local bank screws up, go straight to the Central bank and make a complaint to save yourself being given the run around.
Fees are very low for day-to-day stuff, but high for other things like mortages and loans.