I've only been to Amis, not Osteria. I like some of their dishes very much - mostly the pastas, meat dishes and desserts. Almost everything else I've found I've gotten much better preparations elsewhere in the city at this point - better prep, better taste, better portions. Was very disappointed in their Roman Artichokes as much as I wanted to love them, based on how much I did in Rome. The seafood mixed grill was kind of a joke and way too oily, compared to the excellent ones I've had at Melograno and Salento. But the ravioli I had there on last visit were amazing and the desserts are out of this world good.
Definitely Osteria. Amis is great but less memorable.
At Osteria, you can't go wrong with the best pizza in town and a couple half portion pastas. You might want to call and see if they have the pit roasted suckling pig special - my favorite.
If you're not on a budget, VETRI hands down.