Is premium fuel actually worth the extra over supermarket fuel?

In a national newspaper recently they made a statement saying that branded petrol is no better than fuel bought at supermarkets. I know that you are an advocate of good grade fuel and as such, I have been...

Is the diesel fuel that I buy in a supermarket any different from Shell or BP?

Is the diesel fuel that I can buy in a supermarket filling station really any different that the diesel that I can buy from a Shell or BP garage?

Is Shell fuel really that much better than supermarket fuel?

I've always used Shell V Plus diesel in my Range Rover TDV8, with 160,000 miles on it. My neighbour said it was a waste of money, so I switched to Asda diesel. My car now has worse fuel economy and runs...