at the moment, the biggest problem for the outdoor mural is graffiti... at least in Los Angeles... very big problem...
so your first concern would be - cleaning and graffiti removal.
then the color stability, then the medium life expectancy.
aside from true fresco, the longest living medium would be acrylic.
lime wash you cant quite clean.
also walls fail first, so make sure you do not pain directly on the wall... make it removable...
80% all those are removable (painted in the studio and later installed):
learn fresco at http://FrescoSchool.org
fresco painting video tutorials: http://www.FrescoSchool.com
Fresco School Video Channel
Contemporary Fresco Gazette
commission fresco or mural http://iLAdesigns.com
Contemporary Fresco Painting Resouce Center