For how long are you hoping to go, and who will be going; is it you and a friend, or will you be taking DC too? What time of year?
In countries where distances are so vast, driving is both the obvious choice and at the same time potentially quite tiring. Might you be able to do a bit of both: taking the train for some longer stretches, and picking up a rental car once you reach key destinations? A car gives you the autonomy to stop off and admire surprise views (of which there are many), to spontaneously explore off the beaten track and to switch up your itinerary.
Both Norway and Sweden are known for their natural beauty and wildness -it seems a pity to not give yourselves the flexibility to explore and to get out in the sticks which a car gives you. When home, I literally can't wait to get out into the vast and awesome nature; that's what really sets Scandinavia apart. There are some lovely cities, and you could probably keep yourselves very busy city-hopping, but definitely give yourselves the gift of freedom to explore. Some driving in Norway can be quite hair-raising (Trollstigen, for instance), so be realistic about your nerve and road handling capabilities.
In Sweden at least, nature becomes more stunning the further north you travel, with a sweet spot around 2/3 up. Norway's beauty is more coastal in my opinion, although the interior is quite dramatic too.
If you are concerned about the price of a rental car, the whole thing is likely to feel quite eye-watering. I'm always shocked at prices when I go back. Have you looked into accommodation yet? Hostel accommodation is usually of a high and comfortable standard, and good value. You can get family rooms or private rooms so you don't have to share a dorm (although toilets and showers are communal as are kitchen facilities). If you book early, you can get some great deals.
Make sure you budget to be able to afford nice treats when out and about. 'Fika' is a thing, and whereas coffee refill is often 'bottomless' the traditional artisanal baked goods can be pricey. As can regular eating out.
Wishing you a lovely holiday!