Well the first questions that have to be answered are...
Budget: Just how much are you looking to spend, in this instance that is pretty much nullified by the fact that the X2 and the single core are roughly the same price
Usage: Just how much do you use your computer, and what do you do with it? Gaming, Video Encoding, regular everyday tasks (internet, word processing, that sort of thing)
Since the prices are practically the same, we can get rid of the first question. I would recommend the Dual-Core regardless of what you are doing simply because the single core is only 400MHz faster. So, if an app, or the OS in general isn't utilizing both cores, the single core will be faster. But, if you were to couple that dual core with maybe 2GB of RAM, then no matter what you do on a daily basis, you should see some perfomance benefits over the single core.
Let's say that you do some video ripping and encoding, the encoding stage in particular will eat up some serious processor time... if the app isn't optimized for multi-threading, you can set the affinity to just one of the cores and then keep doing what you are doing with the video in the background not slugging up your machine as badly.
The one place where the single core will win definitely will probably be games, the 400MHz advantage will be handy... but in any games that are multi-threaded, you will be better off with the dual-core.
So the long and short of it is that you should consider the Dual-Core... however, if you are willing to wait a few months, the new Core 2 Duos are coming out and they are supposed to be killer compared to AMDs current offerings.