since you say you are relatively new to the topic, I won't go into great detail on computer performance and capacity - even people who have been in the field for decades still argue at length about it. I'll give you a few pointers and then look at why you might choose one over the other.
There is a difference between Performance, speed if you like, and Capacity, the amount of work you can do. Think of it as an analogy. A truck can carry a vast amount of freight compared with a sports car but a sports car can travel at three times the speed. So if you want to get from A to B in the shortest time, use a sports car but if you want to take a ton of bricks, use a truck. And that's the basic difference you have seen - the "sports car" is the single processor, the "truck" is the quad or higher and a dual core comes mid way between, a wagon if you like.
So, as Bob and others have said, it depends what you want to do. If you are working on a single complex mathematical calculation in multiple steps that follow on one after the other (this is called a single thread), you want the fastest processor you can get, typically a single processor.
If you want to run your web browser, your email client, your word processor and view your latest photos, you would want a quad core processor to run these four independent tasks.
That's the simple explanation, as the chip makers have increased the number of cores (mainly due to the limitations of speeding up a single processor) the application developers have redesigned their programs to use multiple threads in parallel, and so a single application, like video rendering can use more cores in parallel for its multiple threads. The games writers in particular have exploited this technique to use the greater capacity of a multicore processor. Intel have a very good demonstration of Crysis (I think) which can exploit the multiple cores, on a single processor, a dual and a quad. and the screen rendering is able to exploit the multi cores so efficiently, that the dual core completes in half the time of the single and the quad finishes in half the time of that. But this is the exception.
So let's look at performance. It isn't just a case of clock speed. Given two machines of identical design in the same family, say an Athlon 4000 and an Athlon 5000, to use your manufacturer, the performance will closely follow clock speed. But if the machines are not of the same design or from the same family, these comparisons are NOT valid. Performance depends on many factors, the main four (and others may disagree!) are clock speed, Cycles per instruction (an indication of how much work you can do in each clock cycle), the memory bus speed (how fast you can get data from memory into the CPU and back out again into the memory) and the architectural design of the CPU processing pipeline (which indicates the degree of parallelism in each core). The memory system isn't just the RAM, of course, it includes the level 1, 2 and sometimes 3, data caches. So you can get some idea that this isn't just clock speed. The topic is too big to discuss here but I'll give you an example.
When Intel introduced their Centrino package, the CPU component clock speed was much lower than people were used to with the older Pentium design. In fact, the performance of a 1.5 GHz Banias Centrino was very close to that of the 3 GHz Pentium 4 - the difference was made up by the other performance components I mentioned earlier.
To get back to your question, The AMD Phenom is a newer design generation than an Athlon, so some of its extra performance comes from the design, rather than just the clock speed. The designs are not comparable, the Phenon is vastly better. Actually, AMD just released two core Phenoms (though confusingly may have labelled them Athlons!)
and so you should really be comparing a 2 core Phenom with a 4 core Phenom, then my earlier discussion of the number of threads you want to run comes into play.
Trust me, this is a big can of worms you have opened!