If you still wish to run Windows XP on a budget, and you really only use it for general use then a single core processor is fine for this, for single cores I’d be more inclined to go with Intel having found them to perform very well.
Imagine having laptop with two processors, in essence this is what a dual core processor is, dual core refers to a single processor package that has multiple processor cores.
One example of this is excel 2003, we have had many questions from people disappointed by slow excel performance when running reports. Excel 2007 has full support for multi cored processors.
Dual core processors are much faster than single core equivalents
They do cost more, but prices are dropping all the time
They do have slightly less battery life than single core.
They produce more heat due to the design
Software has to be written to take advantage of multiple cores, this used to be more of a problem, but all new versions of any software should support multiple threading, as this is now the norm. (multi threading enables the newer generation of multi core processors to apply more than one core to a task within an application, this effectively halving the time)