Its a rule of physics. A twin-engined aircraft will always be cheaper to maintain than a quad (unless you don't have to pay for maintanence on two of the four engines
). Also, since most airlines are now maintaining thier quads to ETOPS standards, even when they don't have to, this is even more true.
As far as burning less fuel, thats also provable. Just look at the respective aircraft's ranges, then look at their fuel capacity. The 777-300ER has a max range of 8,540 s.m. with a max fuel capacity of 47,890 U.S.g. That's 5.61 gallons for every mile. On the A340-600 (non-HGW), the respective numbers are 8,635 s.m. and 51,480 U.S.g. That's a rate of 5.96 gallons/mile.
That is a very basic calculation. However, taking into account that the 777 has to maintain a larger % of reserves due to ETOPS, and the fact that in flight testing it has proven to be 1% more fuel-efficient than original specs indicated (not taken into account in above), the difference is even greater.
However, you are absolutely right in stating that resale value, as of yet, cannot be determined for either aircraft. Of course, even down the road that will be hard to determine, as Airbus has guaranteed the resale of the A340NG to a couple of customers, so a true market value may never be known.
Honor the warriors, not the war.