[CAVT]

Ok, I know this may sound trivial as many would immediately think "Of course! 64bit is way faster and more powerful than any 32bit".
Well, I'm most of the time a PCLinuxOS user, it's a very nice system, really fast compared to other 32bit systems (even other Linuxes, although I won't claim it's the fastest), and many complaint there's not a 64bit version. However, I came accross this the other days, and here I quote it:

About the 64bit versus 32bit.
I know there differences and I do use 64 bit a lot because of speedy blender renderers. Now let me tell you a fact that actually made me feel stunned.
I have a scene on blender that renders with 1:28 on 64 bits and takes 2:05 to render on 32 bits... This concerns Gentoo, Ubuntu, Mandriva, Fedora, Opensuse... I've tried them all.
Here is the amazing fact... PCLinuxOS 2010 is a 32 bit linux but the did something with the kernel and gcc (it's not only the bfs... I tried it)... PCLinuxOS 32bit renders that scene in 1:15... this is faster then a Gentoo 64 bit with all the custom USE and CFLAGS to help me out.

PCLinuxOS remade linux and set 64bit performace down to it's own feet.

The user doesn't specify his hardware, but anyway, renders are not a piece of cake. Now, in Linux you can use pae kernels which extend the maximum RAM for 32bit systems to 64GB instead of 4GB. My question is then, how convenient is it to use a 64bit system instead of a 32bit? Let's pick the following cases to compare, with the only restrictions of equal CPU clockrate, same amount of RAM above 4GB and same Linux distro in 32bit and 64bit versions:

1) 32bit Processor, 32bit Linux distro with PAE Kernel, software optimized for 32bit.
2) 64bit Processor, 32bit Linux distro with PAE Kernel, software optimized for 32bit.
3) 64bit Processor, 64bit Linux distro, software optimized for 64bit.

Let's suppose also that we are talking of a single desktop machine, budget irrestricted, to work at home, no clusters or similar high-end stations.

Which of these options would have the best performance? Which one of these options would be the one with highest performance/cost ratio?

Naturally I omitted other conditions, so when answering feel free to asume the circumstances. If other UNIX based systems have the possibility of using a PAE Kernel, you can mention them, I simply mentioned Linux because it's what I best know (Windows doesn't have PAE, so don't bother in mentioning it ).