Fuel efficiency of a given type can vary considerably over different distances. The conditions necessary for optimal efficiency also vary widely between types. The jet is best at high speeds and high altitudes, so acceleration/climb and deceleration/descent are important considerations on short journeys. The piston engine is more efficient at low altitudes, but its propellers make for slower airspeeds and this makes long journeys unattractive.
A jet-powered GEV is definitely less efficient than a high-altitude jet, but a piston-engined GEV is in its element and can also make use of ground effect to increase lift and improve aerodynamic efficiency. Theoretical arguments one way or the other are one thing and opinions differ, but whether or not it can prove more efficient for such routes than a conventional airplane must wait for practical demonstration.
But the ekranoplan suffers a curious limitation in that its maximum speed over water turns out to depend on its wing chord, or fore-aft measurement. Wave interference effects mean that the longer the chord, the faster it can go. Above its maximum interference-free speed, its efficiency is among the performance criteria which fall sharply. Thus, the very large but relatively short-range ekranoplan is potentially the most efficient. This was the niche at which the Caspian Sea monster was aimed.
Of course, finding an obstruction-free route for any distance over land is next to impossible.