It really depends on which CPUs they are and what you are using it for. For simple tasks a dual core and a quad core of the same architecture and same clock speed will perform identically as most simpler tasks dont make use of more than 2 cores. It is important to note that differences in architecture mean that the clock speeds cannot be directly compared, the dual core likely gets more done per clock cycle than the older quad does since its a newer design.
There are many cases where a fast dual is better than a slower quad, but there are others where the extra cores of the quad more than make up for the clock speed advantage of the dual core.
What are you using it for and which two processors are they?
The only 2.6 GHz Pentiums that are even moderate recent are the G620 and G622, both based on the Sandy Bridge architecture which has much higher instructions per clock rate than the original phenom architecture did, so in tasks where only 2 threads are used the Pentium should win easily, but in tasks where 4 threads get used they will come out a bit closer on performance with the Pentium using far less power than the Phenom 9500.
Your fastest one right now is the Pentium based system, do you happen to have more specs on the system? If it could be upgraded to an i3 2100 it will be significantly more powerful than the Phenom 9500 in pretty much everything, but for most things the G620 should be sufficient.
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.)