I am referring to apps. I write software and compile for Windows and linux (mostly C++ and Java). The software generally runs faster on linux than windows. Where I write data mining and conversion software with a lot of disk access and memory access linux is measurably faster as it handles disks and memory better (assuming you use a linux disk format and not a windows disk format). In many cases it is a small margin but if I am trwaling through Gbs of data the time saving becomes appreciable. For low-end systems linux is by far the better system. I am involved with a group that 'recycles' old PCs for people who may not be able to afford one otherwise. I have had a modern linux system running on a laptop that only windows 98 would look at. On many of the older systems linux would run smoothly where XP would spend ages swapping data with the virtual disk even in basic office apps.
For the standard office user then there is little difference in speed as generally the slowest thing is the user (but the fact that linux and office are free and linux is far less prone to malware tends to tip towards linux) I play games on both linux and windows and some games actually run faster under WINE on linux than natively on windows.
I am not saying that linux is the absolutely the best OS, it depends upon what you use it for but for a basic office user linux is best suited and cheapest IMO.
I use linux for office, music, web, usenet, email and programming. I use windows for gaming, programming and video (because nothing on linux touches Adobe Premiere yet).
Andy