@ledhead27
I think your are seeing conflicting information because you are not clearly and tightly defining your frame of reference.
Take a jet engine off the airframe and put it in a test chamber where you can change the ambient air pressure/density, and "climb" the atmosphere to simulate high-altitude engine performance. You will get one set of results.
Put the engine back on the airframe and fly it in an "ideal world" in which there are no winds or temperature changes (except ideal lapse rate with altitude), and no particular place to go, but there is drag, and you will get a different set of answers.
Put your 747 into the real world, with real-world changes in all kinds of factors, from winds to baro pressure to air temperature to flight distance to aircraft weight - and you will get yet another set of answers.
As to the first - engines burn two things, fuel, and air. One won't burn without the other. At an altitude where the air is 0.25 the density of sea level, you will "burn" 1/4 as much fuel, and get approximately 1/4 as much thermodynamic output. You can pump in as much fuel as at sea level, but 3/4s of it won't burn, and becomes as (in)effective as water - a cold fluid that doesn't burn, cools the "fire," and provides a bit of reaction mass.
That isn't necessarily more "efficient" - since you also get ~1/4 as much power. Try to run an engine in a vacuum, and you will get zero fuel burn (very efficient) and zero power (not efficient at all).
With small piston planes, you get the same effects. The only difference is, in small planes the fuel flow is adjusted to the ideal ratio with the ambient available air by the pilot leaning the mixture by hand, whereas jets have automatic fuel metering. If your piston engine gets too hot and threatens to start detonating, you can cool it by adding MORE (excess) fuel (richen the mixture) - some of which goes out the exhaust unburnt, but which cools the engine as it passes through (low initial temperature, plus evaporative cooling).
You lean for maximum efficiency (fuel flow best matched to available air molecules) by watching the EGT (exhaust temperature): maximum EGT (hottest "fire") = "perfect" ratio of fuel to air, with all the intake air and all the fuel going into combustion, with no waste of either.
Back to jets - lower fuel burn is not more efficient if you lose something else as well, i.e. thrust or power. But once you put the engine back on the aircraft, and fly it at high altitudes, then you get a benefit in terms of reduced drag. Your reduced thrust can push you as fast or faster through the air, and you still get the benefit of reduced fuel use. The whole system is more efficient, even if the engine itself is not.
Up to a point, where there is not enough air to hold the plane up at even the highest achievable speed, without so much nose-up pitch that your (induced) drag skyrockets. Self-limiting.
As to when flying lower is more "efficient" - efficient meaning total flight efficiency in terms of time and total fuel burn, not engine SFC/thrust ratio at a given moment:
Winds and temperatures have been mentioned as reasons. Trip distance is also important. An A320 will ideally always sip fuel more efficiently at 36,000 feet than at 24,000 feet - yet BA flies Paris-London at ~24,000. Why? Because it is a short trip, and the fuel costs to fight gravity and climb the extra 10,000 feet (and immediately start down again) are higher than the additional fuel burn from staying low. BA's dispatchers and bean-counters have studied the curves and determined that 24,000 or thereabouts (depending on the day's weather) is the most cost-effective altitude, all factors considered.