An Apple/Nintendo head-to-head in the gaming market, or any other market, would be epic. Imagine if TWO first party companies were making yearly unveilings the magnitude of Nintendogs, Brain Age, Wii Sports, Wii Fit, etc.
Unlike Google and Microsoft, however, Apple and Nintendo are not obsessed with posturing for some future face-off. They both aim to create all-new categories and so remain immune from competition and independant from third parties--and are currently doing so repeatedly. If Apple entered the games business, it would likely be with the focus on innovative hardware/software integration that is already the cornerstone of both companies.
And so competition would come from the two companies racing to get new ideas out first, not simply burning through piles of money with a useless game of one-up-manship with no plan to realize the true goal of growth. You might have Nintendo making a motion-controlled motor skills trainer/game for babies and toddlers (with advanced levels for mom and pop), while Apple "counters" with a touch tablet controller that recognizes swipes, stylus, or keyboard functions for PC-trumping content-creation and community features.
I don't know who would "win," but that type of competition would be much more interesting than a race for exclusive FPS's or sports games marketshare.
"[Our former customers] are unable to find software which they WANT to play."
"The way to solve this problem lies in how to communicate what kind of games [they CAN play]."
Satoru Iwata, Nintendo President. Only slightly paraphrased.
