There are only a few routes where you can get EQM's w/Emirates. That being said, you will have a much better experience on Emirates than on Continental. Video on demand, better meals, more room between the rows. You can also use miles to get an upgrade on Emirates if you choose, if you can get it. Continental needs to make a request for the seat. Their First class has 15" monitors and flat beds and their Business class has slightly smaller screens and nice seats. Even coach has better size screens than CO BF. Food is a lot better too.

BTW, in Dubai, make sure that you have a high level MasterCard (world card) if you want to get into one of the lounges at the airport. There is a lounge that will allow you access w/that card regardless of what airline you fly.