Phoronix compared the power consumption of the official ATI Catalyst driver and the Open-Source ATI Driver in Linux. You can check it out over here. The site concludes the power management of the opensource driver needs improvement to put it on par with ATI's driver.
Yesterday we broke the news that AMD will stop supporting the
R300-500 GPUs in the Catalyst driver. There have been well over one
hundred posts in the Phoronix Forums from ATI customers upset with this
decision, but fortunately, there is first-rate open-source support
available. AMD continues to release documentation and code while the
X.Org development community has been hard at work on the xf86-video-ati
and xf86-video-radeonhd drivers along with Mesa and Gallium3D
components. The main problem though is the open-source stack -- at this
time -- providing poor gaming performance, but power management can also
be a problem. In yesterday's article we provided some R500 comparative
2D and OpenGL benchmarks, but in this article are some power management
results comparing the Catalyst 9.2 driver to the xf86-video-ati driver.