Never tried the premium Diesel before other than once when I filled up as it was the only diesel a station had and I was out. I didn't notice a difference, and didn't brim the tank either as it was like 4p a litre more. Needless to say, couldn't get any indication of better economy.
Petrol, now that is different between premium and the likes of the high octane derivatives like Shell V Power, IF you drive a high performance car. Only ever put Tesco 100 or V Power in my Subaru Sti.
Coming back to Diesels, Shell seems to be quite competitive vs supermarket fuel in my area, so try to fill up there if possible. Otherwise use supermarket diesel. I figure as long as I put enough tanks of the advanced cleaning additives in on a regular basis I get the good cleaning effect
Not sure I can feel any difference TBH.