I think that as a career choice, you're better off staying in the US for a dispatcher job. It pays more, and you'll get better job satisfaction, as a dispatcher job in the US is more relevant to the operation than in the UAE.
Right now it might be hard to get one, but once the economy start to pick up again I would go for that.
A major consideration is that a dispatcher position with Emirates for example, does not provide housing, only a housing allowance. And with the rents as they are in Dubai, you'll be tapping into your not-so-good salary in order to pay the rent on your 1 bedroom apartment in an area that's not too hot.
Not sure if other carriers offer better conditions to dispatchers or not. Good luck.