I cannot talk with figures, but as far as I know, 64 bit Ubuntu would run faster for really intensive calculations. Maybe for some multimedia... not really sure
For desktop use, probably you will not notice much difference. The biggest issue some time ago was the availability of flash 64-bit, some drivers which could behave different (i.e. if the were working just for 32-bits), etc
I also have an AMD Athlon 64 and I've tried a couple of times (four years ago) to use a 64-bit distro, and I found it much more displeasant (because of these bits) than the possible benefits I could achieve
What you gain? Speed. What you lose? Somewhat of desktop use. In? Adobe Flash, Reader, Skype, so on. If you dont really need these , you can go for 64 of course. (Honestly I use 64bit for a looong time and I've been fine with it always.) – Apache – 2010-06-25T18:54:26.993
I can't see any real data in the answers, just claims. Can someone please add some benchmars? – Ondra Žižka – 2013-07-22T20:56:16.307