What is the difference between dual-core and quad-core processor in terms of performance?

Will if you compare dual core cpu with quad core cpu from the same architecture,class, family, frequency and company.
Quad core cpu should have more processing power, how much more processing power depends on a Amdahl's law.

When the CPU is running flat out:2.2 x4cores =8.8 GHz running2.8 x2cores =5.6 GHz running That is a simple comparison.
But there are other improvements that are harder to predict, due to access speeds of the internal caches and RAM access speed.
The CPU is not always running flat-out, but scale it to50% and you still have the sames ratios.

In a dual core machine, you have2 processors in a single core.
In a quad core machine, you have4 processors in a single core.
Performance is based on type of server software been used; If you are using SQL Server2008 or above on a quad core processor, software will be able to take advantage of parallel processing using4 processors and response would be faster.
If you want to use quad core processor machine as a hypervisor, you will be able to take advantage of running at least two operating system thereby taking advantage of processing power.
And many more..

Simply: - Dual Core: means can do2 simultanous proccesses.
- Quad Core: means can do4 simultanous proccesses.
The performance is depend on the application and single core speed, for example for linear application - single proccess - like MATLAB, the Dual Core3.0Ghz (each core1.5Ghz) will be faster than Quad Core5.0Ghz (each core1.25Ghz).

Dual cores have two cores, and quad cores have four.
All the cores are on the same chip though.
So, they share the same memory, and data path to the motherboard.

A multi-core chip can execute multiple instructions at the same time.Dual cores have two cores, and quad cores have four.
All the cores are on the same chip though.
So, they share the same memory, and data path to the motherboard.So, a quad core chip may be able to execute the instructions four times faster, but that doesn’t mean it can receive instructions from ram four times faster.Also, the faster a CPU is, the hotter it gets.
Just because the CPU is a quad core doesn't mean it was set to run at the same gigahertz.Consider a manufacturer that wants to sell a4 gigahertz chip, but the core keeps melting.
One could sell a Quad core chip with each core set to1 or2 gigahertz and get increased performance, but still be running each core much slower.
Therefore the chip no longer melts.Software has to be rewritten to take full advantage of multi-core processors.
The operating system might provide a small automatic increase in speed, but you won’t see a4X increase in performance simply by switching to a quad core.Even if the software is rewritten it might not be2X, or4X faster because now the program may have additional instructions added for the sake of figuring out which core is going to access each part of the program.

The difference between single-core processors and multiple nuclei is not measured by the frequency But the ability to handle more data at the same time is no longer the conflict in processing power increasing frequency as it was before, but the multiplicity of nuclei and the method of treatment (based processor architecture) To this point another story Some processors hexagonal nuclei are working hard to approaching the performance of quad architectural nuclei due to the latest and strongest of those processors Quartet And to be able to imagine otherwise.
Suppose there is a horse-drawn cart and we giving another horse that will increase the speed but the drag force is going to go up If we assume the existence of two identical in specifications and one of them works processor unilaterally and the other processor binary, you'll find that a device that works processor binary able to run more than one program at a time without feeling slow, which will face when you try to run the same software on the device first provider processor omnidirectional Core The same difference appears with Quartet processors also What what is already a very simplified, but try to imagine the difference But on the ground topic is a little different Where he must support programs and games for multiple processors nuclei in order to operate at full capacity Where the program by dividing the data into several themes according to the number of nuclei and distributes data on nuclei are processed at the same time Therefore reflected the power of processors Quartet in compression and encryption software, image processing, video, and finally modern games supporting multiple nuclei