I have long wanted to compare the speed of rendering Cycles, built in Blender on different platform - Windows and Linux. Here are the results.
So, there is Lenovo G700M notebook with two operating systems on board: Windows 10 Pro 64-bit version of the 1607 and Linux Mint 18 "Sarah" Xfce (64-bit). A notebook with dual-processor Intel (R) Pentium (R) CPU 2020M @ 2.40Ghz, 4Gb RAM, First video card Intel (R) HD Graphics, the second NVIDIA GeForce GT 720M (2048MB, CUDA Cores 96). The laptop is not powerful, but it is not important for the test.
Test will render in two modes - CPU and GPU, and two system - Windows and Linux.
I downloaded the test file here, have not changed anything in the file, only reduced the number of samples to 100.
The result, as we see, is predictable. The difference of 2 seconds when GPU rendering in favor of Linux is insignificant, though the fact remains. But the gap is almost two minutes while the CPU rendering confidently takes Linux to the winners.
The fact that Linux is quite accurately refers to the consumption of hardware resources does not require proof.
Conclusion: while GPU rendering is not much of a difference which of the two systems to make rendering.
But if you have, for whatever reason, be used for rendering processor - here the choice simple - Linux.