I have to confess that I like the traditional, old school art which in my view ended after impressionists (with rare exceptions). Therefore my impression of these museums will be quite critical.
Although housed in a large neoclassical building of four floors, Ateneum‘s collection occupies only one floor. Other are devoted to public lectures, temporary exhibitions, cafe and museum shop. The only floor with the collection opens up in a very optimistic way with Van Gogh and a few small Rodins, but then it is all about Finnish artists. Most of them painted around the theme of Death and therefore their works are very hard to view for a long time. The slow contemplation of the Ateneum‘s basic collection will not take up more than 30 minutes of your time.
Kiasma is purely contemporary art museum. More contemporary than art, though. The only thing I liked about this 6-story museum is the building itself which resembles Guggenheim Museum of Contemporary Art in New York. Another positive thing about Kiasma is a nice little shop with literature on design in Finnish and English on the ground floor.
I believe that entrance cost of 8 and 7 euros to Ateneum and Kiasma is not really worth the collections they have. But if you are by chance in Helsinki on the first Wednesday of each month, it is justified to visit these art points for free from 5 to 8 pm.