I've just found out that there are two versions of Unreal Tournament 2004, a 32-bit and a 64-bit.
However, in the GOG installer I didn't see an option to select which version gets installed, and as I run 64-bit Vista my OS is capable of running both versions.
So how do I tell whether my install is running in 32-bit or 64-bit mode or does the GOG installer detect the OS type and install the appropriate version of the game?

The GOG version is already patched to 3369 though.

Ah, yeah, but there are 2 versions of 3369, the 32 and the 64 bit one. I think 64bit support was added to ut2k4 only towards the end of it's patch release support cycle, which would be with the last patch 3369.
Exactly, probably not a lot of increase. Back then, the only choice for mainstream systems in the 64bit edition was XP 64bit, which wasnt very good. In his case, if he already has the 32bit version of ut2k4 in vista64, can he install that patch and "upgrade" ut2k4 from 32 to 64bits?

I have no idea as I don't run a 64 bit system myself yet, but it can't hurt to try. Worst case is unreal 2k4 doesn't work and you need to reinstall it.

In light of the above comments from drmlessgames and Ralackk, has anybody tried the 64-bit patch yet and if so does it alter performance or have any bugs/issues?
I'm quite interested in finding out how the multiplayer keys work too, as that's how I found out about the two versions of the game - I asked GOG for a unique key and they sent two registry entries, one for 32-bit, one for 64-bit, with instructions to use the appropriate file.
Now, having looked at the registry entries I can't make much sense of the difference. The registry files are below (obviously I've hidden my unique key with hashes):
The 32-bit file contains the below:
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Unreal Technology\Installed Apps\UT2004]
"CDKEY"="#####-#####-#####-#####"
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Unreal Technology\Installed Apps\UT2004]
"CDKEY"="#####-#####-#####-#####"
The 64-bit one contains the below:
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Unreal Technology\Installed Apps\UT2004]
"CDKEY"="#####-#####-#####-#####"
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Unreal Technology\Installed Apps\UT2004]
"CDKEY"="#####-#####-#####-#####"
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Unreal Technology\Installed Apps\UT2004]
"CDKEY"="#####-#####-#####-#####"
All of those keys are identical as far as I can see. Can anyone shed any light on this?

There is no 64-bit installer for UT2004, there is only a small 10 MB "patch" which adds 64-bit functionality to an existing installation.
You are supposed to install the normal 32-bit version first, patch it fully (irrelevant for the GOG version of course) and finally add the 64-bit files. The 64-bit package contains only a new exe launcher and an OpenAL dll. The 64-bit exe has a file name different from the original 32-bit one, so you will have the option of running both versions of the game. Finally, you might want to create a start menu/desktop shortcut to the 64-bit exe for convenience.
Because you get separate 32- and 64-bit exe files, it's easy to compare performance if you're so inclined. (I've not noticed any difference, but I use the 64-bit version "because I can")
As for the windows registry/serial key issue, I'm not sure what to make of that. I was under the impression that both versions of the game used the same registry area, but I might be wrong. You could just apply both files, of course. A few superfluous registry entries won't do any harm.

I just tried out the 64-bit patch. Initially it ran, but at 640x480 in a window. Using the D3D9 renderer I made it full screen and then tried to change to my native resolution of 1680x1050, but this just resulted in an instant crash to desktop with no error message.
I guess, at least for now, I'll stick to the working 32-bit version.
Oh, and I'm marking drmlessgames with the solution as he is correct, it's by default the 32-bit version of the game (as not everyone has a 64-bit OS yet), and he did say that the 64-bit version was released in a version of the 3369 patch which is also correct.
Oh, anyone know the reasons for the strange registry keys I posted?

Hey man, thank you kindly. : ) Hmm, about the keys, i have no clue, to me both the 32 and 64 bit keys look exactly the same. AFAIK too, cdkeys are usually encrypted in the registry, you can't just read them out. You need a program for that.

So it's not just me then, those keys are identical :P
The files GOG sent me repeat the key twice in the file they provided for 32-bit system and three times for the file they provided for 64-bit system.
I've even looked in my registry for that one key, so I could just enter the new value they've sent me.
In any case, I only requested the unique key in the event that I have difficulties on servers, but as I've only used GOGs server so far it's not been an issue, and I don't expect it to be either, but I have it if I need it.

These aren't encrypted. To get ut2004 working on Linux, I just used the key in the registry, and it's working.
@korell AFAIK, if the cd-key is invalid the game won't start.