The simplest comparison is M5 and 550i.
One car is for all out performance, in a saloon body. The other is effectively a smaller limousine tor someone who doesn't have a chauffeur, nor need the long legroom in the back.
Fuel consumption is irrelevant on a car that loses £13-15k a year for the first owner.
But, as discussed before, the E500 is a V8 for the world market, not for the UK. A default choice for America, when any Mercedes is a luxury decision, and for the Middle East & wealthier bits of Asia.
And, of course, it's a use for the well established Mercedes V8.
Why are 5.5 litre V8's in the States called 550's ? (SL550, CL550, CLS550, E550, S550, GL550, ML550 ? Because the US market loves big engines and holds on to the numbering conventions of two or three decades ago - for Mercedes and BM's. (This is the market where they still lie about "Hemis," and which would have insisted that the fastest Taycan be called "Turbo."
One teensy advantage over the BMW 550i : the Mercedes engine doesn't blow itself up after about 50k miles, necessitating a complete rebuild, usually under BMW warranty.
BMW Settles N63 V8 Oil Consumption Lawsuit | BimmerLife