No doubt, the Opteron's 64-bit architecture is more potent than the Althon XP's. The Opteron takes much of its design from the Althlon core, but it has an integrated memory controller and much larger L2 cache, and of course supports 64-bit instructions as well as 32-bit. It is also designed to reach higher clock speeds than the Athlon, albeit at the expense of deepening the instruction pipeline.
Many of the Opteron's pluses and minuses can be read about on the Tom's Hardware and Anandtech overviews of the K8 architecture:
http://www6.tomshardware.com/cpu/20030422/index.html
http://www.anandtech.com/cpu/showdoc.html?i=1815
It's true, certain applications may be optimized for 64-bit operations, but those are mostly image-processing, scientific or database programs, or programs needing to address more than 4GB of memory at maximum speed. SQL Server, high end 3D Rendering programs or Scientific applications, and imaging programs like Photoshop will probably benefit. For games, I'd say that since modern graphics cards handle most of the rendering and video acceleration duties, you won't see any improvement in that arena, although other areas like the physics simulation or AI for the bots may benefit.
In conclusion, it always is expensive to live on the bleeding edge. Opteron motherboards are currently few and far between, and both the motherboards and cpus have a poorer price/performance ratio than the super-cheap Althon XP's. I'd say for at least until the end of the year, your best buy for the money will be the Athlon XP.
Unless you've got cash to burn, go for a cheap Athlon XP solution, then play catch up in a year or so with newer and cheaper components than are on the market right now. One or two-generations behind the latest and greatest always seems to be the price/performance sweet spot, anyhow.