Cambodia and Laos or only Cambodia?

Alternatively: Laos and Cambodia or only Laos? There is quite enough to keep you busy in Laos for three weeks. Laos is more varied (mountainous) than Cambodia. You can fly directly from Luang Prabang to either Pakse or Siem Reap. Or you can fly from Vientiane to Pakse or take buses all the way. I could suggest spending a week in the far south of Laos, visiting Tadlo, Wat Phu and Si Phan Don. It is delightful. From there you can continue on to Angkor Wat, either by flight from Pakse or overland from Si Phan Don. Long distance buses are the alternative to flying within Laos.
You could spend a week around Luang Prabang (including Vang Vieng if you wish) followed by a week in southern Laos and a week in Cambodia (Angkor etc). If you don't want to set foot in southern Laos at all you can fly directly from Luang Prabang or Vientiane to Siem Reap (Angkor).

I'd say spend your 3 weeks in only one country. There is enough to keep you busy and delighted using the whole 3 weeks in Northern Laos (Vientiane, Vang Vieng, Luang Prabang, Luang Nam Tha and Muang Sing), a combo of north and south (except you will have a long bus ride from the north to the south) or just in Cambodia (Sihanoukville and/or Kampot, Phnom Penh, Battambang and Siem Reap would take all of 3 weeks or more for me). If you must try both then I have done the route of Siem Reap, Kampong Cham, Kratie, Stung Treng and then cross into southern Laos for Si Phan Don, Champasak and The Bolaven Plateau near Pakse. It took me 5 weeks so you may need to cut out a stop or two. However, I travel slowly and you may like to travel faster.

Yep, pick whichever one you want. By the time you figure travel time, missed connections, sleepless nights and bad luck into your itinerary you'll be glad you cut down on travel time.