Assuming you're running x86_64 (amd64) architecture, don't expect a huge difference in performance. This architecture gave things a new baseline for processor features (as compared to 32-bit code possibly going back to i386).
Also, in the 32-bit world kernels and C libraries have already been compiled for different minimum architectures (i586, i686, ...).
Finally, things like games, compression libraries, crypto tools, 3D rendering, ... may already include multiple implementations of core functions that select the most efficient implementation for the current hardware.
But if you must: try to find a reliable standard benchmark suite that measures the performance characteristics that are important to you. Run it many times and look for consistent results.
Compile your own kernel then run it many times again.
If you see any difference, go back to the original kernel and see if the difference remains.
Then go back to your new kernel and see if the difference remains.
Many things can create small differences in measurements, and I don't expect you'll achieve any huge difference.