Isn't that simple?

Asume that your income tax rate is 25%, plus 9% state tax (in california), you are paying 34% less tax on the mortgage interest, which means that 66% of mortgage interest is the real cost.

So the comparison is really :

1. if you keep your mortgage, for each dollar, you pay 66 cents to the bank, government pays 34 cents

2. if you pay off the mortgage, for each dollar, you pay 34 cents to the government for income tax

You definitely pay less if you pay off the mortgage.  However, it takes sizable amount to pay it off, if you can get better investment return on that principle, you may be better off keeping the mortgage and invest the money.