Linux is better than Windows at some things, but in terms of how quick a program can do something, as long as the software isn't really badly written for one operating system, it shouldn't really be that different with the same hardware, coming down to just processing power.

We use finite element engineering simulation software at work (lots of cpu, LOTS of memory, lots of hard disk thrashing) and I've been doing lots of benchmarking between Linux and Win2k versions of software on the same hardware. To be honest I've found little difference between run times on the two, with some cases the Win2k being quicker. The only thing is, the Linux machine is still capable of doing other things and is fairly responsive, whereas the Win2k machine is completely unusable while its doing the computation.