In almost every case, long-range drones use larger propellers than other drones that don't need to travel very far or don't need to fly for very long. I have heard that a major reason for this is because a drone with larger props can be much more efficient than a drone with smaller props. If this is the case, what is the reason that larger props are generally more efficient to use?
Thrust is proportional to the change in momentum of the air passing through the prop - i.e. how much the prop speeds it up.
The power required to do this is proportional to the kinetic energy of the air, which is proportional to speed squared. That 'squared' is the problem.
A smaller prop acts on less air, so it has to speed it up more to generate the same thrust. Half as much air moving twice as fast generates the same thrust, but takes twice as much power.
This explains why helicopters can hover relatively economically, propeller planes only if they're powerful aerobatic models, jets only if they're extremely powerful and carrying a minimum of weight, and no one uses rockets unless they have to.
An explanation for why this is can be found in this Aviation.SE answer: Why aren't large, low-speed propellers widely used?, which I'll paraphrase here.
The thrust a propeller generates is a function of its velocity and geometry. It makes sense that a propeller spinning faster will also generate more thrust. For a smaller propeller to generate the same thrust as a larger one, it needs to spin considerably faster because of its smaller geometry.
The kinetic energy of a rotating object is equal to
I is the moment of inertia (a measure of how hard it is to change the rotational velocity) and
ω (omega) is a measure of the rotational velocity. This means that kinetic energy of the propeller is proportional to the square of rotational velocity.
The same argument holds true for the air that the propellers accelerate, this time by the rule for kinetic energy
m is the mass of air being accelerated and
v is the velocity it's being accelerated to. Likewise, the kinetic energy of the air is proportional to the square of linear velocity.
Because of these two facts, (acceleration of the air ends up being far more important than propeller) the energy the motor needs to put into spinning a smaller propeller to produce the same amount of thrust as a larger one is significantly greater, and thus smaller propellers are less efficient than larger ones.
Comment number 7 at this link is an excellent source (and fairly trustworthy as it was written by Joshua Bardwell).
The main reason specified for the efficiency is that for a given amount of thrust, a larger propeller (on a motor with an appropriate KV) will draw less current than a smaller propeller on a higher KV motor, so there is less sag.
Another thing to think about that isn’t mentioned in the comment is the number of blades used. If you think of most long range quads, or camera quads like a Phantom, Marvic or even a Matrice, you will notice that they have two blades per propeller. This can increase efficiency as it will have one fewer wing-tip per propeller, meaning fewer wingtip vortices and less drag. Multiply this by the number of propellers and the effects add up.