I enjoy both these movies, but I think I enjoy Spirited Away the most. Both movies are very good examples of their respective genres though.
There are a lot of memorable scenes in Apocalypse Now as well as a lot of great actors. It also brings a different perspective to the Vietnam War, with a broader focus on the broader IndoChina theatre, including Cambodia. The final part of the movie in the Jungle, with the natives of the jungle, is a bit gruesome though. Spirited Away has wonderful visuals, an interesting story and well written characters. Also for an anime, it isn't as degenerate or violent as other anime films.
I prefer Spirited Away in this pairing because for me it is a lot more replayable and it is a more relaxing movie. Apocalypse Now is a more serious movie that after the first time is not as rewarding.