Would you recommend that an American rents a car and drives from Copenhagen to Stockholm or takes other means of transportation?
You may like to stop at every little town and village as they can be interesting. If you like to drink beer or other alcohol, driving prevents sampling on the way. (Unless someone else drives.) The train can be really expensive. Flying with no luggage can be cheap, if your hotel will keep your heavy bags until departure. Often I have left mine in places like Russia, Turkey, Greece, and other countries. How many days do you wish to drive? It can be cheaper if you are two, or three. Alone, a train or plane may be cheaper. Last year in Greece, I found I needed a REAL International Driver's License. Only expensive, fly-by-night renters would allow me to rent, so I didn't. We took the train and missed a few places.
Yes, cross that bridge.
SSP Bowl Dude
Take the train.
Why drive yourself when buses and maybe even trains are cheaper?