There is one school of thought that interest and property taxes on a person’s home are one of the few income tax deductions still available and a taxpayer needs as many deductions as possible.
A tax deduction does not reduce your taxes dollar for dollar, but simply by the marginal tax rate of the taxpayer. For example, if you have a $10,000 tax deduction and are in the 28% tax bracket, it would save you $2,800 in taxes. The net effect is that you still spent $7,200. The question becomes: did you get $7,200 worth of economic benefit?
Do the Math like this: let’s say you have a mortgage at 9% interest. You have an extra $100 per month available and want to put it where it will do the most good. If you put it in your savings account, you might earn 5%. If instead, you make an additional $100 principal reduction payment on your 9% mortgage, you will have a 4% net gain without any tax considerations. Regardless of what tax bracket you are in, you will save money in this example.
The answer to the original question is determined by asking yourself if you can earn more in an alternative investment than the rate being charged on your mortgage. If not, then in most cases, you will be better off pre-paying your mortgage.
There is one other consideration you should think about. Will You will need the money in the near future? You may not have quick easy access to the equity. Having that extra $100 in a bank account makes it readily available in case you need it.