A friend of mine who is working for an airline who operates both types of the same series, 330 and 340, gave me a few very interesting figures:
If that airline has to send a 340 instead of a 330 on a route that is not ideally suited to that 4 engines, let's say a 6 or 7 hours flight, on an identical typical payload, the 340 will use about 15% more fuel !
To partially explain that extra fuel burn, the 340 suffers from an extra 8% on the OEW.