ATI do just fine on Oblivion, Have you adjusted your graphics settings to mazimum yet? Oblivion does NOT look worse on ATI than nvidia, and its doesnt seem to perform any worse either Ive ran it on both 8800GTX's and HD4870's the 4870 seems to perform a bit better than the 8800GTX.
If you just installed the game with the new card and it said it didnt recognise the card it would have defaulted graphics to a low setting and you will need to turn things up.
Oblivion does look better with texture upgrades etc but there shouldnt be a lower image quality for the 4850 than the 9600gt at the same settings.
At launch I believe Oblivion was better for ATI than Nvidia.
Another thought if you are using the same system and installation for the 4850 as you were the 9600gt be sure to erase the configuration files under my documents\my games \oblivion folder. The game will recreate these for your new card when you next run it, then reset all your graphics options and see how it looks.