The 4000+ may be the single core version of the Athlon 64 while the 3800 dual core you're referring to is just that: dual core (Athlon 64 X2 CPU). Dual core is better in my opinion.
This is taken from the AMD website:
"The AMD Athlon X2 Dual-Core processor is targeted towards the prosumer & digital media segments. These processors are designed for sophisticated power users who run multiple processor-intensive applications simultaneously. The AMD Athlon 64 X2 Dual-Core processor is also ideal for digital content creation and entertainment consumption.
Today's PCs are multi-tasking environments. With the AMD Athlon 64 X2 Dual-Core processors, the ability to multi-task, such as creating digital content while checking and writing e-mails, while downloading audio files such as MP3s or music downloads off the Web, will allow users to do more in less time. AMD Athlon 64 X2 Dual-Core processors will also deliver superior performance as multi-threaded applications spread from the enterprise server market to the client and consumer markets."
That sums it up. I consider it a high performance processor that is much needed if you work on your computer a lot doing all sorts of stuff on it (games, photo/video editing, watching movies, burning stuff, etc.)
If all you do is surf the net and do basic word processing from time to time, I would get a cheaper single core CPU like an Athlon 64 3000+.