Anytime you have a layover, transfer, etc., there's a chance you'll miss your connecting flight, you luggage (if applicable) will not make your connecting flight, your first flight might be delayed and cause you to miss your connecting flight, your connecting flight never arrived, etc...
non-stop is well worth any added expense, in my opinion.
For example, we flew from South Bend, IN to Chicago, to Honolulu. We had just 10 minutes to make our connecting flight in Chicago. We had to run to another terminal. We made it. And surprisingly, our baggage made it.
On the return trip, we had a 4 hour layover in Chicago before heading to South Bend. Our flight from Honolulu was about 45 minutes EARLY, so we had a 4:45 hour layover in Chicago. Our bags did not make the flight and stayed in Chicago for about a week before they got them to us.
So 10 minutes and they managed to get us and our luggage across two terminals, but 4 hours and 45 minutes they could not do the same.
I shake my head.
I now only take carry on luggage since that experience. I won't do checked baggage.