How to Determine if Processor is 32-bit or 64-bit

Your question is architecture specific. x64 is essentially an extension to x86 architecture. It supports a 64 bit address space. It provides some new instructions and new registers.

You can run 32-bit x86 Windows on an x64 machine. Note that you can't do this on Itanium 64-bit systems.

While some processes my have a larger memory footprint in their 32-bit variants the difference is usually negligable, so I would go with 64-bit for the following reasons:

• You may upgrade the machine to have more than 3Gb RAM at a later date: it will be far easier to take advantage of this with a 64-bit base OS.
• You state you are upgrading from 7/x64: that way installing 8/i386 will essentially be a full over-the-top reinstall rather than an upgrade. While a proper upgrade my leave you needing to reinstall/reconfigure apps anyway, going 64->32 will garantee that requirement.
• Stability/compatability: I suspect that most developers are using 64-bit environments and expecting new installations to be that way, so if there is a difference in stability it is likely to favour the 64-bit environment as that is what is more rigorously tested against. This would be true for both applications and drivers for new hardware.
• If you run very memory hungry applications/services such as someimage/video editing tasks or SQL Server then they will be able to use more than 3GB of memory by use of virtual memory (though this will be slow). In fact the default per-process limit in 32-bit Windows is 2Gb.
• Some applications/services that use memory-mapped files for file access such as some "noSQL" solutions will have files limited to 2Gb in a 32-bit environment even if they only need to have a small part of the file in RAM at any given time.

Of course there are a couple of reasons why you might want to go for 32-bit:

• IIRC 64-bit Windows completely drops support for 16-bit applications so if you have some really old legacy applications this might be a consideration. Of course you could just run those in a virtual environment (using a 32-bit instance in a VM) instead.
• Similarly if you have some older hardware that you wish to use and can not afford to replace with newer kit you might find that good drivers for 64-bit environments do not exist.