Whats better about the Nexus compared to the S2?
The only real advantage is that it's a Google phone and is likely to get software support longer. From purely a hardware perspective the Galaxy S II is the superior device.
Is the Android or Apple app market better?
They both have advantages. Apple's Appstore probably still has the better selection of premium apps. Android Market wins on variety and openness.
Of the devices you listed the Galaxy S II has the fastest CPU, the iPhone 4G the fastest GPU. Performance-wise they're probably pretty close overall.
What has the best looking display?
IMO nothing comes close to Samsung's Super AMOLED+ displays, so the Galaxy S II wins there in my book.