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Since I got my ipad mini, I have not really used my nexus, only for debugging my apps. The battery, screen, speed and so were all worse, and I never got used to the os as much as I have for iOS. If I didn't need an android tablet, I probably would not have one.
Uh, the iPad Mini's screen is 1024-by-768/163 PPI. The first-gen N7's is 1280x800/216 ppi. The N7's screen is noticeably nicer. I can't speak to battery or speed as I haven't had a lot of hands-on time with the Mini, but I will note that the N7's slimmer aspect ratio means it fits nicely in a pocket, while the iPad Mini just plain doesn't.
I have both devices and I can comfortably say Nexus 7's display is much worse. Images appear washed out, it's not as bright as the iPad mini, it has worse viewing angles etc.