We recently learned that it's possible to activate a selection of EA games bought on Steam on Origin. We've successfully redeemed keys for Battlefield: Bad Company 2, Dragon Age: Origins, Mass Effect 2, Dead Space 2, Alice: Madness Returns and Dragon Age 2. There may be more.
In the case of Dragon Age 2, once the product key key had been validated on Origin, it was possible to launch the Steam version of the game from the Origin client, complete with Steam overlay and chat functions.
Not all of the keys we tried worked. Origin didn't recognise product code for Mass Effect, for example, but most of the recently released EA titles we tried could be redeemed successfully. The result is that it's possible to export a portion of your EA games from Steam into EA's new system.
The Origin client already tries to auto-detect EA games installed on the user's PC, it'll be interesting to see if future updates will allow it to recognise EA titles in your Steam library. The fact that Origin can launch the Steam version of Dragon Age 2 suggests that it's already able to reach into Steam's directories.
It's an interesting quirk of synergy in a period of strained relations between Valve and EA. Crysis 2 was removed from Steam earlier this year over negotiations around a DLC exclusivity deal, and current indications suggest that Battlefield 3 won't be available on Valve's service when it comes out on October 25.