Definitions 

An amortized mortgage is a loan where payments are made on a periodic basis (usually a month) over the term of the loan (in most cases 30 years).  Interest is calculated on a monthly basis

A simple mortgage is a loan where payments are made on a periodic basis and interest is calculated on the average daily balance. 

Grace Periods 

An amortized mortgage usually allows for a grace period for payment to be received without any penalty.  (Payment due on the 1st of the month can be paid up until the 15th w/out any penalty)

Since a simple mortgage is calculated on the average daily balance the payment has to be made on time or the following months balance will be higher for a few days and the interest paid will be more.

Which is Better?

This really depends on what type of consumer you are!  Are you one who is punctual every month and able to pay bills exactly on time or even early?  Or are you one who rather enjoys the grace period and pays somewhere in that 15 day window? Are you one who wants to pay off your mortgage early and willing to do whatever it takes?  Do you know the power of compounding interest and how money can be your friend?

If you have an "ok to be a little late" feeling towards bills, then the fully amortizing mortgage is definitely the way to go!  This allows you to take full advantage of grace period. 

Being extremely careful of your bills, paying the day they are due if not earlier could be a good indication for you to choose a simple interest mortgage.

Be honest with yourself!  Your mortgage professional can help guide you through all the caveats of each.  If someone is pushing towards one or the other without be considerate, think about with whom you are working.  Make sure they have your best interest in mind!