One of the biggest differentiating factors from last iPhone to this one is the iPhone 5's longer screen. It's the first thing anyone notices, and the lengthening of the display makes apps feel a lot less cramped. Here are a few of the more popular apps that have already been optimized, next to their old iPhone 4S counterparts.
MLB At Bat
New York Times
And here are a few apps that haven't been updated yet. Not very good.