Diesel oil are designed to deal with soot better than most other oils. They have a higher level of detergents, and therefore a higher TBN. The 15w-40's, as a rule, are more shear stable than a 10w-40. As for the newer 5w-30 diesel oils, it is as stated above.
I recently put Amsoil S.A.E. 30 Diesel oil in my dad's Cub Cadet. It seems to run great. Many people run diesel oils in their motorcycles (higher ZDDP levels are good for bike engines). Just because it says Diesel doesn't mean it is only for diesels, just that it is designed for diesel engines. In some cases, a diesel oil is overkill, but that isn't always bad.