According to Adobe CTO Kevin Lynch:

Flash Player on Windows has historically been faster than the Mac, and it is for the most part the same code running in Flash for each operating system. We have and continue to invest significant effort to make Mac OS optimizations to close this gap, and Apple has been helpful in working with us on this. Vector graphics rendering in Flash Player 10 now runs almost exactly the same in terms of CPU usage across Mac and Windows, which is due to this work. In Flash Player 10.1 we are moving to CoreAnimation, which will further reduce CPU usage and we believe will get us to the point where Mac will be faster than Windows for graphics rendering.

Video rendering is an area we are focusing more attention on — for example, today a 480p video on a 1.8 Ghz Mac Mini in Safari uses about 34% of CPU on Mac versus 16% on Windows (running in BootCamp on same hardware). With Flash Player 10.1, we are optimizing video rendering further on the Mac and expect to reduce CPU usage by half, bringing Mac and Windows closer to parity for video.

Also, there are variations depending on the browser as well as the OS — for example, on Windows, IE8 is able to run Flash about 20% faster than Firefox.

Many of us are not aware of these kinds of differences, because we live in one browser on one operating system, but the non-uniform performance of Flash helps to explain divergent opinions of its merits.

I would be interested to see a similar comparison for Linux, which I suspect would show significantly worse performance than on Windows or Mac.