From a tolerance stack up perspective, integrated headsets have an advantage over pressed-in cup headsets. Fewer parts makes for more certainty of the dimensions of the final product. Of course this depends on the quality of the parts in question. In practice, it likely doesn't make any difference. You'll probably never notice the difference between the two.

In response to the Chris King hype about how your frame will be junk because of integrated headset damage, how often have you heard of this issue? That type of frame has been around a while and I've yet to hear someone say they damaged their frame that way.