I was not convinced by that image so I found a peer reviewed publication that supports it here:
https://link.springer.com/article/10.1007/s12155-020-10183-y
However it appears the above article only used a single sample of RD and PD for each; RD is most likely going to be very similar no matter the sample because it will be 99+% C16 and C18. Petroleum diesel most likely has greater variance.
The difference in density must be attributable to cyclic compounds in petroleum diesel; for otherwise cetane number, carbon length, and energy density are all positively correlated.
Aside from that, irrespective about how you "feel" I prefer numbers if claims as to metrics and numbers in regard to HP or TQ are concerned.
And density is not the only metric that will affect combustion and the resulting power and TQ produced by the engine. Most sources I read indicate that increased cetane number is preferred for high speed diesel engines.
"Higher cetane numbers mean shorter ignition delay and at the same time a better performance of the diesel engine: The injected
fuel burns more evenly and completely, which usually results in higher-quality exhaust air, especially with regard to soot, particulate matter and unburned hydrocarbons."
https://www.mabanaft.com/en/news-info/glossary/details/term/cetane-number.html
More importantly, whether or not I get an extra 2-3% percent of HP, TQ or fuel efficiency either way is not my primary concern over the health of myself or the ecosystem.
Simply from the appearance and smell of petroleum diesel it is often off color and has an odor. Off color can only be impurities. Cyclic hydrocarbons, such as benzene, often have an odor and are more toxic. This is one of the reasons I prefer diesel over gas. Diesel is less volatile and thereby you inhale less of it at the pump. Unless huffing benzene is your thing of course.
In regards to additives, those are often toxic too. People thought tetra ethyl lead was great too, until they realized it wasn't. An extra 1% of anything is not worth turning yourself into a receptacle of toxic amounts of lead, or any of the other additives, for which plenty of evidence exists as to toxicity.
In regards to the ecosystem I will always prefer a product containing no petroleum. It's drilling pollutes groundwater. It's leaks destroy fisheries, peoples lives, and entire coastal ecosystems. The militancy we see in Nigeria is because the Niger River delta has become destroyed by unremediated oil spills caused by Total and Chevron. With their previously rich ecosystem destroyed the impoverished locals who never saw the benefits of those petro$ have resorted to piracy and militancy. This repeats all over the world.
And people want to drill in the arctic? After deepwater horizon I can tell you the outcome...if they can't cap a well in the gulf of mexico in decent time there will be petroleum up welling near coastal cities the world over before they cap a well in the arctic.
And aside from those social and ecological costs, then there is global warming. There is nothing anyone could do to convince me to use petro diesel over RD.
If people are willing to pay for an extra % or two of some metric refining companies will find ways to refine fuels that meet those characteristics out of the same renewable feedstocks because the inevitable truth is that eventually the petroleum drilling industry will cease to exists whether it takes 20 years, 50 years, or 100 years. And I will always use my $ to support industries which share that conviction such as to promote and accelerate that occurrence.
Chemical and liquid fuel refining will continue using alternate feedstocks such as waste and ag by-products, both of which have less risk and capex involved in their supply chain.