Which is one has a better performance?
It depends on the type of hardware you're running. If you have at least a dual core processor and 3-4 GB of RAM, your computer should be capable of running any OS pretty fast. Then it's just a matter of which OS would be easier for you to use and which you would prefer.
As others have said, it depends a lot on the configuration, but broadly speaking, Linux requires a less powerful processor. which by extension would suggest that for a given processor, it would run faster.
Depends on what you are doing. There's no clear cut winner either. Linux is pretty generic. There's hundreds of different versions that look different, run different, include different programs and bundled software. It's hard to say for sure. A lightweight Linux distro will probably give you better performance browsing the web and playing media files than Windows (unless you optimize an XP cd with nLite and remove various features and tweak settings)
I agree with sneakily that it does depend on configuration and that Windows 7 loads very quickly. It also depends on what Linux system you are talking about. Ubuntu? Red Hat? Redora? Historically Linux has loaded much quicker and been more stable than several other operating systems, but with all the programs and interface modifications from some of the current versions, some of those advantages are debatable. I'd say Windows 7 and, let's say, Ubuntu, go head to head on speed, but Ubuntu is more lightweight.
This completely depends on your system, the configuration, and the software you're trying to use. If you have a modern computer (less than 2 years old) with decent memory (2gb or more) and you don't clutter up your startup with useless programs, Windows 7 is plenty fast. Most Linux Distros boot up fast, and run fast depending on what you're trying to accomplish... but if you don't know how to use them properly (mainly file structure and priviledges/permissions, software install/uninstall), you can end up wasting a lot of time trying to figure things out instead of doing things. I'm actually a big fan of both Linux and win7 myself, and both have advantages, disadvantages... but as for actual speed, your OS isn't going to make much of a difference compared to your hardware components, drivers, and software configuration.
For boot time, Linux (specifically Ubuntu 10.04) is definitely faster! For me, native Windows programs (e.g. Windows Explorer) always go "Not Responding" or are just really slow/buggy. The fastest program in Windows must be Firefox/Chrome.