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I’m not sure I understand it properly: does a 64 bit OS run/compile code faster than a 32 bit OS on the same system?
We’re using 64 bit OSs where I am and it seems to only cause compatibility issues with legacy and proprietary software. (We’re running Ubuntu 9.04 Jaunty amd64)
I will restrict this answer to x86-32 (IA-32) vs x86-64 (AMD64), as I believe that’s the question you’re actually asking.
At the processor level, there are a few advantages. First and most obvious is the expansion of the per-process virtual memory to a much wider range of 48 bits. (64 is allowed in the architecture but not required, if memory serves.) That enables applications to use a lot more of the system’s memory available to them, as well as opening up a lot of space for things like memory mapped files that operate on virtual memory that isn’t linked to real memory. It also opens up a lot of space for the OS in question to work, as it doesn’t have to share your 4 GB limit for its data. In short, applications and the OS can make better use of your machine’s resources.
Additionally, the AMD64 architecture addresses one of the biggest problems of IA-32, which is the utter lack of registers. In fact it doubles the available registers, which is a huge win for some types of code. (Actually it’s a win for almost ANY code, but some applications suffer from the increased memory cost of 64 bits and it evens out.)
On the Windows side, MS has taken it as an opportunity to break a whole bunch of historical compability problems. It’s not a clean break from the old world, but it’s a start. I don’t believe Linux suffers from the same problems to begin with, and I don’t have much perspective to offer on their 64 bit advantages.