Pro screen is better by far but feels cramped. Air has a higher resolution. Basically it depends what's more important to you.
Air screen is also less glossy.
I thought a higher resolution screen means better screen as with the retina.
Anandtech did a complete review of the air and I would advise you to read it. http://www.anandtech.com/show/6063/macbook-air-13inch-mid-2012-review
Both machines are very good, but which is all around optimum for your needs should compare all the features not just the screens. If you do go with the air try and see if the place you get it from will let you see if it has a samsung display, read "The Display" section in the review as to why.
Great machine, enjoy!
I thought a higher resolution screen means better screen as with the retina.
Well if you actually read the display section, you'll see that the author says he can't tell which is which after calibration.
Shortly after that review, Mountain Lion came out with new default profiles, greatly improved for the LG screen.
That issue is over now, and you'll notice that the corresponding thread https://forums.macrumors.com/threads/1389918/ has been dying slowly since then.