Judging from some of these responses I wonder if a lot of the responders have even used both, at least for any length of time. I have both. I have two 17" MBPs and a 13" Air. I had a 13" MBP for 9 days and exchanged it for an Air. I like the Air better, but that's just my personal needs talking here.
There's absolutely nothing wrong with each. They are different in several ways, none of which are bad. The Air is only a compromise in one, read this, ONE way - screen color gamut and accuracy. If you require a LCD that has a color output you can calibrate such as photo and video editors then you really need to stick with a MBP. I have a MBP for my photo editing and wouldn't even bother attempting this seriously on my Air.
For everything else those, the Air is pretty much equal or superior. You don't get an optical drive and if a built-in optical drive is necessary then get the MBP. If you don't need it then the Air will probably make you happier.
Get the Air unless one of the following situations is important to you:
* You need more than 4gb or ram
* You edit photos and need a calibrated output
* You require an optical drive that is built-in
For me I find I like the MBP for home use and wouldn't take anything but the Air outside of the house.