A quad core has 4 cores, a dual core has 2 cores. The quad core has more cores available to help your programs run, IF your programs need them or can take advantage of them. For instance some apps use only one core and won't run any faster whether you have 1 core or 50 cores. Other apps can make use of more cores, 2 or 3 or more. There used to be a lot of arguments on these forums as to which was better- dual core or quad core. It has been proven with benchmark tests that many or most current games will run faster with more than 2 cores.
At one time you could get dual core cpu's that ran at faster clock rates than more expensive quad core cpu's. In this case depending on your apps you might be better off with the faster dual core than the slower quad core. Current generation cpu's have gone past this and the faster ones are automatically quad core.
The other variable is that different generations, models and brands of cpu's all have different internal workings and will run faster or slower than others at the same clock speed. So you can't compare AMD and Intel processors because they have different internal efficiencies. Also you can't compare a current Intel i5-2500k with a previous generation i5-750 or the generation before than Q9650. But you could compare say a Q9650 Intel quad core with an E8500 Intel dual core because they are of the same generation.
And the last little influence is that some cpu's can overclock better than others, so you could have 2 cpu's with similar stock speeds but one would be capable of a lot faster speed with overclock than the other one.
If you really want to compare different processors the best way to do it is to look for Tom's occasional articles "best gaming cpu's for the money". And also consider the needs of your software and whether you need 2 cores or 4 cores.
(For desktop computers I'm a believer in 4 cores, but in laptops there are heat and battery advantages to sticking with just 2 cores if that's all that you need.)