You're opening a big can of worms here, mate. Here goes with my findings.
I have tried various big names and the main supermarkets too. I've driven 600 miles exclusively on each brand. That's Aberdeen to Dover - often.
I travel overland to Croatia and Bosnia 4 times a year - same route - same speeds, same weight. The distances are recorded from Sat-Nav, and the fuel is brim to brim.
I have tried to be as objective as possible.
I shan't bore you with numbers and miles, but here are my conclusions.
I have concluded that supermarket diesel is cheaper because it does not have the extra additives. During the fuel drivers strike it became glaringly obvious that nearly all the fuel we use comes from a very small number of refineries, and you can get tankers from Esso, Shell, BP, Tesco, Asda etc. all loading up at the same depot. Its the brand specific additives alone that are different.
Supermarket diesel is just not worth it - I get less mpg on my journey with it -therefore using more of it - so there is no real saving at all.( Perhaps someone doing only a small annual mileage, in towns only, might get different results.)
Worse though - I get plenty black smoke on overtaking with Supermarket diesel.
I have found little difference between Tesco & Asda, but Morrisons is by far the smokiest.
The conclusion of all this comparing is that I now try to use Shell V-Power diesel whenever possible - I collect the points which do actually mount up quite well. (double points for V-Power)
Little performance difference between Shell and BP Ultimate. Elf/Total/Fina's Excellium is pretty good too, but I encounter less of them so difficult to do a long journey using only Total.
In Europe I stick with Shell or Total, but in Austria there is the best diesel of all - OMV Sprint Diesel - the extra cetane I think does it.
I also now use 300ml of 2-stroke per tankful and the beast ticks over quieter and (perhaps psychologically) seems to run better.
Being a Scotsman I am still sorely tempted by offers such as Tesco's 5p off if you spend £50 in the store etc. However I am resisting.
Hope this is of use to you.
Regards, Sing