This is a great question that has likely been asked since the invention of mortgages, and it will likely continue to be asked forever.
The answer to that question is very personal and needs to be tailored to your situation. However, three common factors come up quite frequently when I am discussing this issue with a client.
Emotions surrounding debt. Some individuals simply despise all types of debt and want to get out as soon as possible. There is also a peace of mind that comes with paying off a mortgage early. If you feel strongly about this from an emotional perspective, that should drive the decision.
Risk tolerance and risk capacity. If you are comfortable taking financial risks and can afford to take more risks with your money, overpaying on your mortgage may not make sense for you.
Current mortgage interest rate versus your expectations for investment returns elsewhere. If you expect that you can get better rates of return on your money by investing it than what your current mortgage rate is, it may make sense to not overpay on the mortgage. That is assuming that you will save and invest the money you would have used to overpay on the mortgage.
You should consider whether or not you really would save instead, as it is the key. If you believe you would find some way to spend the money if it is available, it may still make sense to overpay on the mortgage to save the interest. From that perspective, overpaying on the mortgage can be a way to help force yourself to save by building home equity.