I get to be the first one to say that I'm holding on to my iPad 3 and to suggest that you do, too
I have an iPad 3 and a retina iPad mini. There's no question that the new hardware is nice and fast. I handled an Air in store just for kicks and in terms of weight it definitely feels more like a mini. If I were using my iPad as a work device and/or bringing it everywhere with me then my 3 would be an Air right now. (But the big iPad stays at home, and the mini is what gets used at work, hence why the mini was upgraded.)
I use my iPad for email, light web browsing, reading, and the occasional game. For the way that I hold it the weight is a non-issue. While games perform better on the newer hardware and the iPad 3 has a tendency to heat up with extended play time, I don't game enough to justify an upgrade.
If you use your iPad like I do, then the iPad 3 is still good enough. It's far enough from the Air that you would notice and appreciate the differences if you did upgrade, but not so far that switching between the two makes one feel clearly inferior (in my opinion and for my usage).
If money isn't an issue and/or your iPad usage could benefit from the upgrade, then it's a fine upgrade with improvements that you'll notice and appreciate. If money is more of an issue and/or there isn't a "must have" feature on the Air then hold off for another generation or two (or three). The iPad 3 is still a wonderful, very usable device with a lot to offer.