Pros for rail:

Faster
Cheaper (unless 3 or 4 of you can cram yourselves and all of your gear into a sub compact)
Very convenient — city center to city center, often walkable to hostel and major sights
At least one train an hour (often 2,3, or even 4) between these cities so nearly as flexible as a car
Overnight trains save time on longer journeys

Cons for Car
PARKING
Navigating city centers to get to the sights (better to stay and leave car in suburbs and use public transit)
Hidden expenses
Pros for car
Great to explore rural areas, get to trailheads for hikes
,Avoids logistics problems of getting to the extra cave or waterfall since you won’t need to rely on public transit in less populated area
May be the best way to get to some specific place.

My advice: while you won’t have any trouble navigating between cities, if your itinerary is just visiting these cities, stick to the train.

PS: With 2 days per city, you definitely don’t have time to drive. You need an average of three days per city to cover travel time (by train) and to even get a feel for the place. Overnight trains both ways is the only possible way you’ll get to Venice on this whirlwind trip.

Venice and Amsterdam are both built on canals. There are no streets in Venice and only a few in the central part of Amsterdam.

That would be a crazy itinerary, 6 cities in 12 days. travelling between these cities already will take you at least half a day each leg.

I would really pick three or four cities. Paris, Amsterdam, Munich, and Venice would be more than enough.

Paris – Amsterdam: Highspeed train
Amsterdam – Munich: Plane (Lufthansa has 99,- euros roundtrips, use only first leg) or city night line train
Munich– Venice: train
Venice – Paris: plane (train takes too long)