Yes I think we are talking about 2 different options - or even 3.I had in mind grinding a slot so that when you use the breaker afterwards, you have more chance of a neat straight edge on the trench beside the house. The thinner the concrete, the more likely it is to work (unless you hire a big road menders cutter)
I think you are saying take the full depth of concrete away from the house for a narrow trench. I am saying take the lot up. Or another option just angle grind a V grove to take the water away.