Sitting on the fence.....
Emirates NBD is a pretty good local bank by all measures, with a great ATM network in the UAE, and plenty of support from the girls in the EGHQ branch.
That said, as an expat who is looking for an international bank, I would recommend HSBC over the others. I've govt HSBC (Premier) and the services they provide are solid - they are definitely not the cheapest, they do sting you with fees and have appalling forex rates, but they have a good ATM network both in the UAE and globally, a good website for various types of electronic transfers and transactions, and pretty good digital FOB security.
I think the key with using HSBC is not to setup anything from scratch with the back office staff in Dubai. Get your accounts set up in your home country, get your ID and your relationship status validated at home on the worldwide computer system, and then come to Dubai and open the account you need.