I received a new iPad today (along with a 1080p Apple TV) and whilst I don't want to review it in detail (there are plenty of other reviews) I will say that the screen is absolutely incredible. Whilst most 3rd party apps are not retina-ready yet, those that are look stunning. I actually used my iPad to answer my emails today as it looked so much crisper than my iMac!
Anyway, one of the things that has interested me is how iPhone apps would look on the new iPad. Bearing in mind that there are 4x as many pixels, I assumed that Apple would use retina versions of iPhone apps scaled up. As you might recall, the original iPad and iPad 2 would use regular iPhone apps and scale them rather than using the retina equivelants (something I've written about before). I could understand this for imagery but the keyboard and text looked horrible when scaled making any app that wasn't a game pretty much unusable at 2x mode on an iPad.
Fortunately this has changed with the new iPad. Apps are stills scaled, but the fonts are much crisper as is the keyboard.
To demonstrate, I've tested a couple of apps on iOS 5.1 on both the iPad 2 and new iPad and listed some screenshots below. These have been scaled down to fit the page so you will need to click / tap each one to load up the fullsize versions. You won't notice the difference (aside from some colour improvements) unless you view at fullsize as they look pretty similar when scaled down.
The new iPad is on the left - iPad 2 is on the right.