This thread is full of mis information, so I will try and fix that. It's a long post, but adresses everything I have seen so far.
Efficiency and profitability
First let's talk efficiency in the terms of airlines and their aircraft. To measure aircraft on a level playing field against each other, you must look at their CASM (Cost [per] Available Seat Mile). The lower the CASM, the more efficient the plane is. CASM can be altered in two ways: adding more seats to a given aircraft (spreading the same costs over more tickets) or by reducing the overall cost of operating the flight.
However, the profitability of a route is based off of the RASM (Revenue [per] Available Seat Mile). The higher the RASM, the more money the airline is making. RASM can be increased by a two methods as well: The Airline can cut overall capacity on a route and charge more or they can offer a more premium product and charge a premium price.
Both of these metrics are fluid as the number of tickets sold and for what price on each individual flight will change each.
The 747
The 747 was initially very popular due to its range. At the time it came out, no other plane had the range it had. Many airlines also bought them just for the prestige of having the largest aircraft ever in their fleet. American Airlines was one such airline, but quickly sold them off as they did not make money with them. Many airlines that did not need the capacity of the initial 747's, but instead the range, eventually replaced them with the longer range DC-10's or the L-1011's or even the 747-SP (shorter fuselage/less capacity but the longest range of all three wide bodies).
However, as the 747 progressed through its various variants, so did air travel from the flying public. The travel demands where able to expand and then keep up with the capacities offered with the 747.
747 vs A380
In the 90's Boeing and Airbus both were involved in a joint project that would have created an all new plane larger than the 747. However, Boeing decided that it did not feel the market was big enough for this plane so they backed out of the partnership.
Airbus decided to continue on and eventually they came to the idea of the A380. Meanwhile, Boeing bet that the market was not big enough to justify a brand new VLA, so they decided to focus on developing an all new medium sized aircraft that would travel near the speed of sound (the Sonic Cruiser). However, the Sonic cruiser did not pan out as planned so they used that research to form the basis idea of the 787. Because they were focusing on a smaller plane, they decided to just upgrade and stretch the 747 in the form of 747-500/600. However, the airlines did not respond to the -500/600 well and eventually they started the 747-8 program as a low cost development that would share commonalities of the 787 to keep them in the VLA segment of aircraft as the A-380 had been officially launched by then.
The 747-8 initially was off to a good start. In fact, Emirates was one of the few airlines that had direct influence on the design of the 747-8 along with Lufthansa and two others. Lufthansa wanted a 747 that had a larger capacity but Emirates wanted a plane that had more range than the 747-400. Boeing decided to go with Lufthansa's request, but also added more range, however it was not enough for Emirates, so they chose the A380 which had a slightly longer range. British Airways was also set to place a large order for the 747-8 as well, but Airbus at the last minute offered a ridiculous lowball offer that swung the decision to Airbus.
Boeing has publicly stated that they have turned down requests for the 747-8 from airlines as they wanted them too cheaply. However, with the 777-9 on the horizon, the 747-8 is all but done.
A-380
For the time being, the A380 is in fact the worlds most efficient airliner, until the Boeing 777-9 enters service. But as pointed out, it is only efficient if it is flying full as the costs to operate a flight does not vary much.
Airlines are running their A380's seating anywhere from 407-538 passengers. The lower capacity layouts are very premium heavy, meaning they have more premium seats than standard economy seats. These seats will net more income however, so a plane carrying fewer passengers could actually make more money than the same plane flying with more seats.
The A380 is a profitable airplane for the airlines that actually need it. However, like the 747's of the past, certain Asian airlines have ordered it only for the prestige as their competitors had already ordered it.
There are no A380's being flown strictly on domestic routes like some 747's were. All of the 747's used as domestic planes have all been replaced by versions of the 787 or 777.
However, for Airbus, the A380 program is a loss making program. Some people here were talking/asking about it breaking even... Right now, every A380 that rolls off of the production line COSTS Airbus to produce and deliver. In late 2015, the production process will finally reach it's break even point before finally moving ahead into the profit range; meaning the price the airlines are paying for the frames will be more than the price Airbus is paying to make them. ONLY then will the entire program begin to head towards the total break even point of all the production and development costs, which initially was set for 200-250 airframes, then later to 400 and finally it was said they would not disclose the official number, but it was projected to be in the 600-700 airframe range.
The A380 will never break even. Remember how I said earlier about air travel catching up with and then keeping up with the 747 development? Well as of now, it has failed to do so for the A380.
The A380 is a great plane, but it came too soon. The 777-9 is poised to become the best 747-400 replacement on the market. It will offer the same passenger capacity, the largest cargo capacity of any passenger airliner all while burning less fuel and having only two engines to maintain.
The argument of 2 vs 4 engines doesn't always come down to fuel burn. The A340 family is almost as efficient as the 777 on a fuel burn basis and even beats it in some cases, at least so I'm told, but it is the maintenance costs associated with having two more engines that makes it so much more expensive to operate.