What to choose – a garage in the house or a carport next to the house?

We are currently in the process of planning our house. We have a construction window of 9m (width) and 12m (length). The default is a parking space by the house or in the house. Now we are thinking about whether to integrate the garage into the house. Then we could use the 9m width for the whole house. But is that a significant additional expense?

Or are we planning some space next to the house for a garage/parking area. This area next to the house could also be used as an additional outdoor seating area for table tennis, etc. In turn, the living space would be slightly smaller on the first floor/home would be narrower.

What do you think? Which option is better?