I had no problems restoring data for Angry Birds using TiBu. Try to re-install the BusyBox within TiBu (menu -> Problems) and restart tibu. "bad" versions of BB can mess things up.
For those of us that have used "Apps 2 SD" in the past, and have moved apps like Angry Birds to the SD, the app doesn't restore / install from the market. I've seen this behavior with a bunch of apps i moved to the SD card previously. Eagle helped me out when I flashed the ROM
The solution: Unmount your SD card. Install from Market. Remount SD Card. Move App to SD card (last step optional)