Now I'm not saying Hamilton or Button are at the same level, but the partnership could be seen as similar to Senna and Prost at McLaren*....
For me, I expect Hamilton to have the upper hand in qualifying. Button may have cleaner, more measured races. Pace wise, given a car that works for his style, Button is fast and can be on Hamilton's pace, but if the car is not to Button's liking I think Hamilton's driving style is more suited to compensating for the car. Overall Hamilton will have the edge over Button, but the actual results could go either way depending on tyre management, crashes, reliability, etc..
* Although I only started following F1 in '91, which was after Prost left McLaren, I've just finished reading 'Senna Versus Prost' by Malcolm Folley..a pretty good read.