The physical SIM size will be different between the two.
Your best bet is to activate the Air, and use it's sim to bring internet over to the iPad 2 using a SIM adapter. I don't believe your iPad 2 SIM will give you 4G or LTE. That said, using the newer sim in your old iPad should work fine (for 3G speeds).
I currently swap my 4S sim into my iPhone 4 (3G only), and have no issues when using a sim adapter.