It depends.
- When I impregnate 9 different women, will I get a baby in 1 month ? Nope. Some things can not be parallelized. The same is true of some algorithms. For some problems, you can not write programs that make use of a 2nd, or 3rd core. Those programs will run just as fast on a CPU with 1 core, as on a CPU with multiple cores.
- Sometimes algorithms can be created to run in parallel on multiple cores. But the software developer has not done that yet. If you think of a particular program that you are concerned about, you need to check if it can make use of multiple cores or not.
- How fast does each core run ? CPUs run at a particular "frequency". An internal "clock" ticks once, or a few times per nanosecond. Every time that clock ticks, the CPU performs a step in a computation. The faster the clock, the faster the CPU does its computations.
- How effective does a core run ? During each clock-tick, a CPU does a little part of work. Some CPUs can do a little bit more work during once clock-tick, than other CPUs. This can make one CPU a little (5-50%) faster than another CPU that runs at the exact same frequency. (This is called IPC, = Instructions Per Cycle).
- And then there are more details. Cache. Bus-speed. Memory-speed. Etc. Many small improvements on the overall architecture that can allow the CPU to keep running more efficiently. The result will be that some programs will run faster. Again, if you want to know how a specific program will behave, it is best to (read a) benchmark (about) that specific program.
- Are all the cores really full blown cores ? Intel has hyper-threading. That means that an 8-core CPU has 4 real cores, and 4 extra virtual cores. The virtual cores do make some programs (10-40%) faster compared to just 4 cores. But not for all software. AMD has a different architecture, when there are 8 cores, but only 4 FPUs (floating point units). So if you run a program that does mostly integer-computations, an AMD 8-core CPU can be twice as fast as a 4-core CPU. But if your program does mostly floating-point computations, then an 8-core CPU might be just as fast as a 4-core.
So lots of details to be aware of. On average an 8-core will be faster than a 4-core. But not always. And sometimes the 4-core might even be faster. The smartest thing to do is: check benchmarks of your favorite programs (and favorite games), and base your decision on that info.