In theory you can make more by putting the money in something with higher returns. Plus, you get to deduct a portion of the interest from your taxes, and in theory putting the excess money somewhere else is additional diversification.

AKA instead of paying your mortgage at 4% interest, you invest it in something that make 5.5% and gain an additional 1.5%-a few percent in taxes+a few tents of a percent in taxes on the 4% interest.

Frankly, its a good theory, but given the volatility of the markets, its hard to guarantee your going to actually come out ahead. Particularly since interest rates are generally computed by people who are looking at the risk/reward factors, and the interest rates have to be high enough to attract the risk adverse capital.

The one thing that is for sure, is that you should never really be sending early payments to your mortgage company despite all the financial advisors telling you to to do so. If you want to pay your mortgage off early your better off putting the money in a low risk investment and then paying it off when the outstanding mortgage balance falls below the value of your savings. That is because overwhelmingly your just giving your mortgage company an interest free loan due to the fact that they apply the over-payment to the final payments and don't adjust the amortization schedule.