Which park is more interesting for a two-day/one-night visit, Litchfield or Kakadu? Which sights should I see during these two days?

They are both completely differnt types of landscape, so it probably depends upon your interest/likes.
Kakadu is mainly flat. It is very interesting provided that you take a professional drive and boat tour so that you learn all about it.
Where as Litchfield is all about the escarpment, with many spectacular waterfalls, cliffs, rivers, etc.
I personally loved Litchfield and would have no hesitation is recommending it.

Kakadu is Australia's largest nat'l park, and is comparable in size to Yellowstone and is equally as varied. I don't think it is correct to say it is "mostly flat". Wetlands do account for significant area, but there are also upland areas with impressive escarpments and huge waterfalls. Getting to some of these places in the Wet Season can be impossible...so time of year is important.

Litchfield is appreciably smaller than Kakadu. It too has beautiful waterfalls, but no where near the scale of Jim Jim and Twin Falls in Kakadu. I thought the magnetic termite mounds in Litchfield were impressive too. Swimming holes in Litchfield are popular with locals because salt water crocs do not penetrate that far inland. From what I remember there was not as much in the way of aboriginal rock art in Litchfield as there was in Kakadu.

Despite my high regard for Litchfield, Kakadu would be my recommendation. If you can, take a 4WD tour out to Jim Jim and Twin Falls. By all means visit the escarpment overlooking the floodplain at Ubirr just before sunset. Spectacular, a very moving experience for me. A Yellow Waters cruise another day will give you good looks at crocs and other wildlife.

If you only have time to do one park, do Kakadu. You'll see fantastic aboriginal rock art, and the trip on Yellow Waters is great (lots of birds and crocs). Also the boat trip on the East Alligator river is worth doing.
As Ralph says, Ubirr Rock late in the afternoon is spectacular.

Thank you very much for your helpful input. Do you think it is necessary to go with a tour from Darwin or will it be possible to do short tours in Kakadu and travel in our own car? We prefer not to be with a group for 2 or 3 straight days, if possible, but are willing to do it if it is essential.

We drove to Kakadu in a campervan. Did an all day 4WD tour to Jim Jim and Twin Falls and took two cruises: Yellow Waters and East Alligator River. The rest of it (Arnbangbang Billabong, Nourlangie Rock, Ubirr, etc.) we did on our own.

It's an easy drive from Darwin into Kakadu. There's a roadhouse midway (I think at Mary River) for a coffee break. You could also stop at the wetlands viewing area.
You could then book day tours and be picked up at your hotel, however you may find that you can do quite a lot of the sightseeing in your own car. Ubirr Rock and Nourlangie Rock are easily accessible by car, as is the Yellow Waters area.
Check with the visitors' centre in Darwin - they may advise that you book any tours in advance to be certain of getting on them.

Thank you for your suggestions. I now have only one full day in Darwin. What should I do in this case? Is Kakadu too far for a one-day trip?
If I do go to Kakadu, which cruise is better to take Yellow Waters or East Alligator River?

This may be backpeddling on my earlier comments, but with just one day, I'd suggest Litchfield as it is so much closer to Darwin. With one day, and considering it is ~3 hr one way to Kakadu, a Kakadu visit would be very rushed indeed.

Ralph, thank you for your comment. Could you tell me which cruise you liked more, Yellow Waters or East Alligator River? I understand that both of them are in Kakadu but I would like to undertand all of my options. Thank you!

Yellow Waters cruise is run by the national park rangers and concentrates on showing you the birdlife and animal life in Kakadu. The East Alligator cruise is run by a local aboriginal community and talks about the customs, weapons, tools of the local people. You will probably see some crocodiles but if your interests are the wildlife, then take the Yellow Waters trip.

Alisa: both cruises were great. Very different for the reasons marg states so it's tough to compare. But if I had to make a choice, the East Alligator cruise would probably be my pick. We really enjoyed the aboriginal aspect and our aboriginal guide playing his didgereedoo as we cruised along. Saw several crocs on the river bank. The river is also quite picturesque as it winds is way along the base of the rugged escarpment. As I recall, the East Alligato cruise departure point was relatively close to Ubirr, my favorite spot.