I have both an 11" air and iPad. I am a developer so the iPad's main purpose is testing apps on actual hardware.
But I found the two do compliment each other, while still overlapping in some areas. If there is a long article I want to read, I send it over to the iPad. Pretty much anything involving reading goes to the iPad. If I find a video I typically play it via the iPad as it actually handles 1080P content better than my Air most of the time. (Plus it can actually display it all.) Anything involving typing is on the Mac. So essentially, most work stuff I do on the Mac, most recreational computing is done on the iPad. With the exception of email, which I like to do on the iPad for some reason.
I do sometimes use the iPad as an external monitor for my Air which works well, as the screen sizes are very similar. So you have an ultra portable dual screen setup.
At some point in the future I am going to compliment them with a 27" iMac. While the Air is great, sometimes I just need a bit more computing power. I have been dabbling in a little video editing, and the Air works, but since I have to use an external (USB...) hard drive it gets slowed down reading from the disk. Rendering speeds are adequate though for the short videos I work on.
There are a lot of small uses that my iPad fills in, that I could never use a laptop for. For example, chord charts for when I play guitar at my church. With the iPad I can swipe between pages easily and it easily rests on a music stand. A laptop would need a different stand, plus I would have to fumble about with the keyboard/trackpad to scroll around and have to worry about battery charge.