native 64 bit applications do run 2x faster without tweaking,
sorry, that is not true at all, 64 bit application will NOT run twice as fast . this is a common misunderstanding
Assuming the app does not need more than 2 Gb address space (=most common applications), If you install on a certain system a 32bit Operating system and use a 32bit application then this will run just as fast (and maybe even a tiny little bit faster) as the 64 bit version of that application on the 64 bit operating system system. This is true for linux, windows, etc etc
32 bit applications on a 64bit windows system take NO advantage of the 64 bit windows os besides a better memory management allowing 32bit apps to use up to 4gb address space (in most cases) .
Running 32 bit windows applications (who need less than 2gb address space) on a 64 bit
windows system will often be (a bit) slower than running the same 32 bit application on a 32 bit windows.
Only when the application actually needs more than (on windows) 3 gb of address space (= not the same as ram) then 64 bit windows is needed (assuming your application is than also a 64 bit application). By default you can go only up to 2b address space on 32bit windows, but you can up this to 3gb in most cases who need this.
On linux there is mainly a performance gain by using 64 bit linux and 64 bit applications when your application uses more than 3gb (or 4 - depends on the distro) Gb of address space because the memory management will be simpler, but it will also not run 2 times faster than a 32bit app on a 32bit Linux.
bottom line: for apps that do not need several gigabytes of address space 32bit is fine, if you use 64 bit OS then make sure you use also 64bit windows applications for the best result.
the only real BIG advantage of using 64 bit OS and applications (!) is that your application can address lot's of GB's of address space . On windows you NEED to use 64 bit for above 3gb (there is one exception - PAE but I wont go into that here) and Linux full 64 bit will be having faster/better memory management above x GB.
Edit: above a summary, there is a huge difference between OS's and there is stuff I left out to avoid more confusion and note that address space of a process (!) is the real limit here and this is
not the same as ram.
32bit windows
as a system can in general (there are exceptions) not use more than 4Gb of ram, 32 bit Linux can in most cases use more than 4gb of ram
If you need to buy a new windows license then get 64 bit win 7, if you have a 32bit XP license already then this is fine in most cases and buying a 64 bit windows will not bring huge benefits for most tasks.