Thorough as he is, I think there may be other factors that weren't specifically mentioned by DTLW.
Damiao appears to play for Brazil as a kind of pivot around which the other forwards operate, in a similar way to Lambert I suppose. His contribution is greater than just his goals as his continued presence (when fit) in the Brazil side would attest. Osvaldo is more of a shoulder of the defender kind of striker as I understand it, so comparing their goalscoring records is quite unproductive. Osvaldo's attitude has also been questioned, and though some claim that's been overstated, there's no smoke without fire and so on.
They're both international class strikers so I'd be happy with either, but Damiao would be my preference for his versatility and because I believe he would better hit into our system.