Most trips end up a mix of the two, and the mix is worth thinking about rather than defaulting to one.
A campsite pitch in Finland runs roughly €25–40 a night for a camper with electricity, more in July at the popular places. For that you get mains power, a dump station, fresh water, showers, usually a sauna, and somewhere the children can be noisy without it being a problem. If you are staying two nights or more, it is almost always the right answer.
Parking free costs nothing in money and something in logistics. You are running on the leisure battery, so heating and the fridge draw down; you still need a dump station every three or four days; and you need somewhere you are actually allowed to be (see our note on what everyone's rights do and don't cover). For a single night between two driving days it is ideal.
The rhythm that works for most people is two or three nights out, then a campsite night to empty, fill, charge and shower. That keeps the costs low without the trip becoming an exercise in tank management.
In winter the calculation changes. Heating runs harder, the battery does less, and mains power is worth paying for. Campsites open year-round are fewer, so look ahead rather than assuming.
One thing that is not a saving: parking somewhere marked no-overnight because it is free. Those signs generally exist because the previous visitors left grey water or rubbish, and getting moved on at 11pm in the rain costs more than a pitch.