HD is likely straight group 3 which is also 100% synthetic while ss has some pao but the quantity can depend. You'll be giving up a bit of everything with the HD but not like it would matter. Many engines go north of a half million miles on cheap conventional with very minimal wear and blow by.
Me being me I'd run either delvac extreme or Valvoline heavy duty diesel both in 15w-40 if i wanted something great for a great price. That's much better than the red jug conventional motorcraft diesel these usually get and they still last long enough. Walmart has both ready to ship for free for 22 a jug. Delo XSP is also good and I bought a few gallons a while ago. The Mobil one is available on shelf but the Valvoline one is online only. But if you want Amsoil get either.