6 core vs 4 core processer

It depends on the 6 core or 4 core processor and the workload you are putting it under... and what you consider to be a core... and what those cores consist of

Right now for single-threaded applications a duel core i3 processor can keep up (or beat) with a 6 core AMD desktop processor, but the 6core AMD chip will run circles around an i3 on games or other heavily threaded applications. Similarly, a lowly single core desktop processor can keep up with the processing prowess of an 8core ARM bigLITTLE processor in almost any workload you throw at it simply because it is so much more powerful.
On the other hand, in a server application it is often more advantages to have lots of little cores instead of a few big cores, and so new ARM architectures with tens or even hundreds of cores are starting to make their way into the server world. Really it brings more of a GPU scale to the CPU world.

But, due to your grasp of the English language and your powerful mastery of punctuation, I am going to go out on a limb and assume you are talking about building a computer for video games
Today, right this moment, the best (and most cost effective) processor you can get is an Intel 4000 series i5. Pick up a cheap i5 if you are building a simple game rig, or a K sku (and z87 motherboard and aftermarket heatsink) if you are looking to overclock it. Games typically don't take advantage of hyperthreading and don't typically use more than 4 cores, which makes most i7 processors useless for games even though they are more powerful, and makes the smaller but more numerous cores on an AMD chip a little less effective. There are cheaper processors on the market which are capable of gaming if you are on a tighter budget, but the i5 is the sweet-spot.

BUT (and it is a big but) this may not be true much longer.

Right now the new consoles are all running AMD 8 core processors. Next gen games designed around consoles may be able to break the traditional 4 core limit that seems to affect current PC games, which would in theory make 6-12 core processors much more useful for games than they are today. This means that there could be some major advantages to getting an AMD chip in the near future compared to an Intel chip in spite of the lower per-core performance.

However, there is no guarantee of this in real world performance. Desktop processors are substantially more powerful than the new consoles, to the tune that even a simple duel core desktop processor could keep up with the 8 core chips used in consoles on most workloads. This may mean that while next gen games CAN take advantage of more cores, it does not mean that they WILL use more cores; nor does it mean that they would NEED to use more cores to be played effectively.

So I guess the simple answer is this: Right this moment there are few advantages (in general) moving from 4 cores to 6+, but in the near future (less than a year from now) this might change and 6-8 cores may become the new standard.