I designed dry/composting toilets as part of a project with small, rural landowners in eastern Ecuador. Because of the high humidity and rainfall, the design we used was to maximize airflow past the material. In wet places, urine-diversion is absolutely necessary. You can see some pictures of our design on our blog:
http://bickfordsabroad.blogspot.com/2013/03/pooping-green.html
We ended up using a dessication process first (storing the material dry for 6 months). A man near where we are living has done microbiological studies and finds the local bacteria, worms, etc. die in about 4 months of holding the material dry. The extra 2 months are insurance.
After that point, we advocate a hot compost of the material. We haven't had any problems with the composting process with the piles uncovered, provided they are large enough. Rainfall where I am is over 3 meters spaced evenly throughout the year. It is rare that we go for a week without some kind of rain.