The Burj & Emirates Palace are clichés of luxury and for me fail to deliver. I am not sure why you limit yourself to these choices as the Emirates have much better options. In Abu Dhabi, for instance, Qasr Al Sarab by Anantara is probably the best desert resort ever created. The Yas in Abu Dhabi is also a unique experience and even The Fairmont there is a great choice.

In Dubai, O&O The Palm is really special, especially if you opt for one of the Villa suites and do not stay in the main building. O&O Residence & Spa (50 suites) is also one of Dubai's top offerings - much more high-end than the Burj.