Various things cause differences in performance. In general, compiling for the specific processor that you have is probably one the smaller contributors, but, there are certain special cases in which the additional instructions (e.g., SSE 'add-ons') make a considerable difference.
These are usually things like photo and signal processing and in those special cases, the instruction set add-ons can be very worthwhile, but I have to emphasise that if you don't have any of the special cases the gain is much smaller. Probably not even noticeable to a casual user, but measurable in benchmarking results.
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