I have been banking with National of Dubai since day one here (seventeen years have passed!!).
Very few hickups, but you do get frustrated at times with their banking system and policies. They have a good online system, credit cards, and overseas tranfers.
Banked briefily with LLoyds, very good indeed.
ABN-AMRO ... very basic bank. I closed a credit card account with them, after many billing problems.
I have heard horror stories about HSBC, Mashrekh (spelling?), Dubai Bank, and even though I never used those, stay away from them.