I try to do via stays first as my nights are very variable. Last year i qualified on both but would rather get qualification done with as quickly as possible.
Case in point my trip to NYC next week, 5 nights, 5 different hotels...not a huge fan of the hassle BUT i get extra diamond amenities, and I get to stay in hotels I never stayed at before as I try to get to the 50 unique hotel award (having already received my 25 unique hotel award).