First of all, I have owned both engines. They are both great engines if properly maintained. My short explanation would be that if you have CAT, you have tons of immediate get up and go from a stop and that power will come at a price and that price is the lack of fuel milage.
If you have a Cummins, it will take its good old time getting you moving on down the road, but it will move you down the road and reward you with much better fuel milage than the CAT.
If some sort of a problem shows up with either engine, yes, it will cost money.