Having been to both, I'd definitely pick Luang Prabang even if it's harder to get to.

Chang Mai has got a lot of good sights and it's a good jumping off spot for trekking, but Luang Prabang is just so tranquil and beautiful. There are so many great sights to see, and a short walk can take you down the Mekong river, on a hill overlooking the city, or out in the countryside surrounded by the real Laos. It's a spectacular place.

There is also enough of a tourist infrastructure so that you can get comfort food if you're craving traditional French or American cuisines. Lao food isn't super crazy either, just rice and meat.