I just looked at the website and the handles appear to be identical on both types. If there are any differences they would be minor.
The D5 is significantly more expensive and you have to decide if it's worth it. Five vs. three layer construction. I have several pieces of the SS and never had an issue with the three-layer construction's being inadequate. I'm sure the five-layer would perform as well.
The only physical difference I see is the D5 has a pouring lip on its pots and pans where the SS does not. That is a material benefit.
Either way you will be pleased with their performance. All-Clad is good stuff.
Before you buy, check out this site: Cookware & More - Outlet for All-Clad Irregulars
It's an All-Clad outlet that sells cosmetically challenged cookware at a significant discount. They are currently having a Spring Sale that offers an additional 20% discount.
Best of luck!