Here's some info from Caldwells speed shop website.
Q:
I use Rotella or other diesel oil in my classic or high performance car. Doesn't this provide the ZDDP protection necessary for my car?


A:
Diesel oil is engineered with a higher amount of dispersant and detergent to deal with the increased amount of soot and other hydrocarbon by products in a diesel engine. This high amunt of detergent can increase the decomposition temperature of the ZDDP reducing its effectiveness as an anti-wear agent. Diesel engines are manufactured with this issue in mind. Gasoline engines are not.

Typically the viscosity range for diesel oil does not include the very low 5w and 10w values. Tighter bearing clearances in passenger automobiles often require free flowing oil, diesel engines typically have larger bearing clearances minimizing the need for free flowing oils.

Diesel oil is not optimized for film strength as needed in high performance and classic automobiles. For a given viscosity high detergent diesel oil has a lower surface tension and lower shear strength which can cause increased bearing wear, especially in high reving engines.

Diesel oil has metallic based detergents which can cause excessive ash deposits (sludge) in your engine. These deposist in worse case scenarios may cause detonation especially in high compression or supercharged applications.

Newer diesel automobiles are being designed with catalyic converters the implication is that ZDDP levels will be reduced in diesel oil making the discussion a moot point as ZDDP is removed diesel oils will become totally unacceptable.