Update
As @Zeus has pointed out correctly: Drag coefficient stay constant in my scenario, not drag -- I've updated the explanation accordingly. Sorry for that blunder. The conclusion does not change: Engines with constant PSFC only have an advantage when flying slowly and get worse much quicker than engines with constant TSFC -- but actual engines are mostly in-between these days.
As others have pointed out already, the important thing to note is that propellers have (roughly) constant PSFC (specific fuel consumption per power output), and jets (roughly) constant TSFC (specific fuel consumption per unit of thrust).
(The second thing of note: quoting equations which include unit conversion factors is dangerous, and doing so without specifying which units are used is doubly so.)
Power is thrust times velocity, which means that although a propeller can have a much higher propulsive efficiency (propulsive power vs shaft power), it also scales quite differently with speed, even ignoring the fact that propellers have difficulty operating above Mach 0.6:
Assume we have a series of aircraft, each designed to fly at a particular speed (all well below the speed of sound), with the same glide ratio and the same weight. This means they all fly at the the same drag coefficient, and the required thrust scales with the square of speed. Now we decide which kind of engine to use for which one of them.
Let's design a family of jet engines, each of which delivers a certain thrust, and all of which have the same constant TSFC. This means 1 Newton of thrust costs the same amount of fuel per second, independent of how fast you're going.
The fuel flow would of course still increase with the square of velocity because you would need more thrust the faster you're going. And that means that fuel burn per distance travelled would increase proportional to speed. Most jet airliners are actually flying faster than their best glide ratio (= lowest drag coefficient) would suggest, because that minimizes fuel per second, not fuel per distance. They're even flying a bit faster than what they@d need to do to get minimum fuel per distance because for an airline, time is money. That's why they're burning a bit of extra fuel in order to arrive faster and do more flights with fewer aircraft.
Using propellers with reciprocating engines, though, although they're converting more of the shaft power to thrust, the fuel flow through the engine scales with power, not thrust, and power needed for constant thrust scales with velocity. So doubling speed at equal thrust requires twice as much fuel per second, but since thrust increases with the square of velocity, fuel flow actually scales with the cube of velocity. So fuel consumption per distance scales with the square of velocity, proportional to drag (still assuming the same drag coefficient for all aircraft, of course).
That's why the most efficient propeller aircraft would be flying at the minimum drag, i.e at their optimum glide ratio, fairly slow.
Going faster gets expensive quick.
So however efficient your propeller is at some (low) speed, the faster the aircraft for which you want to decide on an engine, it will eventually be worse off than a jet because its fuel per distance quadruples when doubling speed, but the jet's only doubles. At whichever velocity our fictional jet engine and piston/propeller get equal fuel economy, the move to the next-faster airraft with a propeller will be twice as expensive as with the jet. And at the same time, the same aircraft with a jet will be flying faster, too.
That's the reason why piston engines with propellers are the weapon of choice for long-endurance flights, where distance covered is less important than time afloat, or where costs are more important than speed. In such cases, a jet would get much worse range!
However, most larger propellers are driven by turboprops these days, and turboprops do not have constant PSFC, since they have a turbojet core providing the shaft power, which benefits from the increased pressure of air in the intake at higher velocities. And modern high-bypass turbofan engines don't have constant TSFC, either, since they have more losses in the bypass duct at higher velocities at constant thrust. In fact, an extremely high-BPR turbofan starts to approach the characteristics of a comparably low-BPR turboprop (except at large Mach numbers, but we're still ignoring that here).
Conclusion
It's dangerous to confuse TSFC and PSFC. An engine with constant PSFC (old-fashioned piston-driven propeller) might fly a lot more efficiently at low speeds but gets worse quicker than engines with constant TSFC.
Because nobody (except for this guy -- who is amazing) wants to take days to finish their intercontinental flight, and because propellers don't work so well at higher Mach numbers, commercial long-range flights fly at speeds at which jet engines (that is: Turbofans) use less fuel per distance than propellers with reciprocating engines, and they get higher range in those circumstances. For high-efficiency flying over long distances, where speed is not that important, however, Propellers are still popular, and have better efficiency. See for example auxiliary engines for sailplanes, or most military transport aircraft. For the latter, range is everything, speed (and noise...) are secondary. However, since those are built to military specifications, they're not that useful as civil cargo aircraft, and since the civil cargo aircraft market is very small, most of it is covered by converted passenger aircraft. If there were dedicated civil cargo aircraft of similar size as long-range passenger jets, they'd probably fly much slower and use turboprops (noise regulations permitting...).
Aside
Another issue with piston engines is that their performance reduces the higher the fly, as the air thins. This issue can be reduced by adding a turbocharger, but a jet engine already is essentially a very big turbocharger with a turbine attached. The other advantage of jet engines is their power-to-weight ratio. This is why e.g. most helicopters don't use piston engines and have turbines instead.
