I decided to just use Thief's built-in automated benchmark, since we can't measure performance with AMD's Mantle API using Fraps. Unfortunately, this benchmark is pretty simplistic, with only FPS average and minimum numbers (as well as a maximum, for all that's worth.)
Chalk up another shocking win for Tonga. The R9 285 beats both the R9 280X and the GeForce GTX 770 in the Thief benchmark. Good grief.
Notice that the R9 285 doesn't fare as well with AMD's close-to-the-metal Mantle API as it does with the game's default Direct3D mode. By contrast, the Tahiti-based Radeon HD 7950 benefits a bit from the switch to Mantle. Looks to me like Mantle support for the R9 285 may not quite be ready for prime time.