If you compare benchmarks where multiple generations of GPUs compete against each other, such as the Passmark benchmark, later AMD GPUs seem to have a better ratio of benchmark scores to theoretical computing power (as given on http://en.wikipedia.org/wiki/Comparison_of_AMD_graphics_processing_units )
Radeon HD 3850: 427.5 GFLOPS, Passmark score of 532
Radeon HD 3870: 497.3 GFLOPS, Passmark score of 744
Radeon HD 4850: 1000 GFLOPS, Passmark score of 1043
Radeon HD 4870: 1200 GFLOPS, Passmark score of 1361
Radeon HD 5750: 1008 GFLOPS, Passmark score of 1399
Radeon HD 7750: 922 GFLOPS (at 900 MHz), Passmark score of 1624
The 38xx surprise by bucking the trend - maybe some AMD developer had a bright moment there? But in general, drivers for current cards seem more efficient. In the 7750, the change in architecture may have helped.
For Linux in particular, the open source drivers are gradually getting closer (at least to the AMD Catalyst driver). For some older and presumably simpler games, the reviews on http://www.phoronix.com/ already show 80% of the performance of Catalyst. In other, more demanding, tests they still suck but the long term trend is encouraging.