Taking your points backwards, there is no reason for a quad to divert to an airport with one engine out (unless there has been substantial damage to the airframe due, say, to uncontained turbine failure). Take a look at the 180 minute exclusion areas and you will find that there is virtually no difference between areas of operation between a quad and a twin on almost every route around the world, as there was when the 120 minute rule was the maximum.
As to fire, the maximum cruise speed of both the 777 and the A340 is Mach .85 (the 777 long range cruise speed is Mach 0.025 faster than the A340) but experience indicates that the A340 can maintain maximum cruise for longer with less fuel burn than the 777 and the A340 descent profile from altitude is steeper than the 777.
As to the 777 not being reliant on one generator; when an engine is shut down, the associated systems are either shut down (if the cause of the failure hasn't already done it for you) or transferred to be driven by the other engine - but this is done sparingly as you are adding load to a system that has already been robbed of 50% of its power capacity.
Either way, the basic premise remains - an A340 crew would only think about diverting for a one engine shut down if it became necessary due to colateral damage, a 777 crew would HAVE to as soon as the shut down happened.