I had a new Z4 M40i before I got my 840d. I miss the engine from the Z4 slightly which is the same unit as the M340i, but apart from that the 840d is the better car in every way possible! It is significantly more comfortable and grown up to drive. The standard equipment is very generous too with lots of bits I didn't have before like the HK speakers, Head up display and Comfort Access.
Try them both and see what you think but unless you're desperate for the slightly better performance/ soundtrack the 8-series is better IMO.
Oh and on the fuel economy I'm seeing about 35mpg long term from the 840d whereas the Z4 sat at 28mpg so a slight improvement there
