Q:  Is it wise to pay extra on your house each month or to send in a 13th mortgage payment to attack the principal?  Or should I invest that extra money and then use the profits to pay a large amount on the principal to get my house paid off more quickly?
A:  Here’s one way to look at your situation.  Putting your money into the stock market or other investments by its very nature includes some risk to your capital.  When you pay down the principal owed on your home, there is no risk – the total amount you owe goes down every time. 
I guess the bottom line is that you need to ask yourself, “What is my ultimate goal here?”  If you’re working toward paying down the loan on your house more quickly, I suspect your best move is to use your extra money to directly reduce the principal you owe on your mortgage.
Considering the unexpected twists and turns our economy has experienced the past few years, there is something to be said for the peace of mind that comes with eliminating your debts.  You’ll just sleep better at night knowing your house is paid off.