In terms of booting up, shutting down, waking up, opening applications, saving/opening files the MBA will be faster.
However when doing stuff like exporting iMovie files, playing games, encoding video via handbrake, your MB might be a little faster.
I went from a Unibody MBP 2.26Ghz C2D with 4GB RAM to my 13" MBA with 2.13Ghz C2D with 4GB of RAM and haven't looked back since.
Actually, I would hazard a guess, based on Anandtech's own benchmarks, My own Macbook air, macbook pro, and my experience putting together another 13 inch 2.4ghz macbook pro with a micron c300 ssd, and an intel G2 ssd....
Boot and sleep would be faster on the macbook air, due to the integration into firmware, ie less checks and recognition tests needed to boot.
But actual usage, the other SSDs are just as fast if not faster significantly. The anandtech benchmarks clearly show that.
Even among SSDs I get different performance. For example I had a sandforce based drive and by specs it's faster than my intel x-25M G2, but usage wise, the x-25m boots faster on the same machine and gets better scores (WEI scores and some crystal bench scores). I would hazard a guess that using an intel drive would actually lower the boot time that anandtech saw, but would still be slower, ie 15 seconds for the macbook air, but something like 18 seconds for the intel drive.
So it would probably save you alot of money to pick up a larger fast SSD, if the weight was not an issue for you.