sod all difference - even if you trust Jaguar's claimed weights:
XJ 5 litre S/C SWB - 1,945 kg (to EU standard)
S500(/550) SWB - 1,995 kg
In practice the Jag will be around 100 kg heavier than claimed.
The standout in the comparison with the XJ against the new S-Class is not the weight but the engine and hence fuel efficiency. The supercharged V8 in the Jag drinks fuel for fun, whereas the 4.7 V8 bi-turbo in the Merc, even with the about to superseded 7-speed auto, is an order of difference more efficient, whilst being even faster:
XJ 5 litre S/C SWB - 11.6 l/100km, 24.4 mpg, 20.3 US mpg, CO2 270g/km, 0-62 mph 4.9s
S500(/550) SWB - 8.6 l/100km, 33 mpg, 27.4 US mpg CO2 199g/km, 0-62 mph 4.8s
With the 9-speed auto in 2015MY and the S400 3 litre V6 bi-turbo in the range there's gonna be some serious butthurt with the 'lightweight' Big Cat.
So, you assume Jaguar's official weights are wrong, yet you completely trust MB's fuel economy claims? Speaking from my own extensive experience of the big three German manufacturers, the MB S 350 BlueTEC was by far the furthest away from the official claimed figures when I drove it. Audi A8 3.0 TDI quattro was around 45 mpg over 2,000km. BMW 730d 40.1 mpg over 4,000km. S 350 CDI BlueTEC? 31.0mpg over 1,800km.