It depends a lot on what you want to get out of your vacation. Universal has some great rides, but my mother isn't thrilled about the whole open air, turn you upside down, make you scream kind of ride. So that basically leaves me and my father to do what we like and my mother gets a nice tan. There are some nice shows but you cannot do all of Universal in one day. If you do go, one day for IOA and one day for US is enough for my family. We really don't intend on going back because our family was split up most of the time and we really prefer WDW over anything else. Though we do miss Men In Black and the Spiderman ride.
Now if you are looking for more variety and things that tell the story, go with Disney. Again there is no place like it, and you can never see and do everthing in a park if you are just there for one day. You can hit the highlights in each of the four parks and make a great day for each of them. It is all in what you are looking for: Disney Magic, theming, and variety or US thrill rides. If you decide to both, you might be really tired!
Depending on what you would decide to do, if you decide to do just Disney, I would stay on property, but if you want to both you might want to stay "in between" US and WDW. It is all up to you in the end, so whatever you think will make you happy and enjoy your vacation is what you should go for!