Since most HDEO's are dual-certified such as CI-4/SL, that's a good question. Here is what a HDEO has that a regular "starburst" oil will never have:
1. Extra additives to deal with high soot environments in modern emission-controlled HD diesel motors: detergents/dispersants far beyond what just an SL oil can provide.
2. Extra additives to deal with newer HD diesel motors with redesigned pistons that moved the Ring Land much closer to the Crown Land: the additives prevent Top Grove Fill and ring sticking/breaking.
3. Extra protection at high temps, as most HD diesel motors are turbocharged. In particular, the Ring Land area can see +600 F under full load and 100% turbo.
4. For regular 15W-40 oils, the polymer additives are carefully selected to minimise shearing, as most HD diesel motors operate HEUI, which places severe shearing forces on an oil.
5. All other things being equal, the slightly heavier 15W-40 will lower oil consumption while having minimal or nil effect on fuel economy.
I've run HDEO's in all my personal cars and have noticed minimal to nil difference in fuel economy. I would like to try this theory out on something like a Honda Civic that already gets 40 MPG, just to see if lighter oils are CAFE nonsense or truly energy efficient.
As an extreme example, I bought new a 1990 Toyota 4Runner with 3.0 V6. Running Mobil 1 5W-30 and then Mobil 1 15W-50, there was NO difference in fuel economy. But the 15W-50 made the motor almost silent, no "tickticktick" noises whatsoever.
There has been some concern about the additives in HDEO "poisoning" the catalytic convertor and O2 sensors. Since most HDEO's carry SL ratings, I very much doubt that.
And since a 5W-40 or 15W-40 will usually cause a dramatic lowering of oil vapor passed into the exhaust stream, the cat and O2 sensors should last longer.
In the end, I would say a HDEO is far better in most engine environments. At the very least, the motor will stay cleaner and use less oil, even if you extend the OCI.
Jerry