The main reason for choosing super petrol is increased performance. There should be a small fuel economy gain but not enough to compensate for the higher cost of the fuel.
Diesel is different. The main reason for choosing a super Diesel is not performance. It's about increased protection of the engine and its very expensive and complex after-treatment system (i.e. the exhaust catalysts).
In Europe, the Cetane rating of super Diesels is typically only 1 point higher than that of normal Diesel. There is little if any direct performance gain to be had here.
Because Diesel engines are used in trucks, there can be an expectation that Diesel engines are rugged, tough, bomb-proof. This is very much not the case. For Diesel engines to work, the dimensional tolerances, clearances, surface finishes, loads and pressures are all much higher than in typical petrol engines.
Then there is the matter of complexity. A petrol engine is typically a relatively simple, inexpensive beast with a single exhaust catalyst. A Diesel engine is more like a complex gas processing plant that happens to produce some power as a byproduct. Instead of a single exhaust catalyst, a modern Diesel may typically have an oxidation catalyst followed by a particulate filter followed by a NOx filter and possibly an ammonia filter. All of these various filters have to be kept working in their own working temperature range in order to function. There will also be at least 1 or possibly 2 different routes to recirculate exhaust gas back into the air intake - and the turbochargers have to cope with it too.
All of this is made possible by a sophisticated control system which keeps the engine running in an operating window which suits all the elements of the engine & its catalysts.
However, the engine wears with time and use, as do the various fuel injectors, catalysts and turbochargers. And all the time, it is having to digest various impurities and unwanted contaminants. These vary from bacterial bugs from bio-diesel to soot, ash, partially burned fuel and acidic water. Over time, the engine and its exhaust system gradually bung up with this gunk unless you protect it.
What the super Diesels from the branded oil companies do is to help the Diesel engine and its aftertreatment system get rid of the gunk, so preserving the performance.
One of the better known issues with Diesel cars is caused by only running the car for short journeys, especially when using basic diesel. With a cold engine and a cold exhaust system, the particulate filter traps the soot but never warms up to the point where it can regenerate. So it clogs up until the owner faces an eye watering bill for a new DPF. Using super Diesel (at least 1 tank in 4 or so) and going on some longer runs of 20+ miles at higher speeds literally cleans the system out and preserves its performance.
The reality is even more complex & nuanced than this, but I hope this at least gives a flavour of what's going on.
Having said all of the above, I would caution against dumping in half a pint of "Diesel cleaner" additive into a fuel tank. This type of product does contain aggressive additives in higher concentrations that will take the engine outside the carefully controlled operating window that the car maker knows is safe for both the engine and its exhaust system.
So in summary: use super petrols for performance but use branded super Diesels for protection of the engine and its exhaust system. Aftermarket, DIY Diesel cleaning additives are best avoided.
Hope this helps.
Now, back to the turntable and some tunes, FT