I don't think I need to upgrade my 3 either. As everyone has observed, the Air is lighter, thinner and faster. But its not that much lighter, thinner, and faster than the 3 such that I think my 3 needs replacing.
I run iOS7 on my 3, and it works fine. There is a (barely) perceptible lag on some of the transitions, but nowhere near enough to be significant.
When the next iPad Air comes out, next year I will reconsider things then.
I note that there has been some mention in this thread of a potential Spring release for the next Air. I do not think that is likely. The iPad release schedule has been an annual schedule with the exception of the 3. Many customers (including me) felt ripped off when they replaced the 3 within 6 months, particularly when the new iPad had twice the processing power. I don't think they'd make that mistake again.
My advice to the OP - Upgrade to iOS7, and enjoy your iPad 3 having a new lease of life. Forget about the perfectionist's complainants of lag in transitions. In the real world for almost all users, it still works brilliantly.