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).
(Second: quoting equations which include unit conversion factors is dangerous, and doing so without specifying which units are being 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 much 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:
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 a little faster than their best glide ratio (thus lowest drag coefficient) would suggest 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 it's 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 increasing with the square of velocity, fuel flow actually scales with the cube of velocity. So fuel consumption per distance is scaling with the square of velocity.
That's why the most efficient propeller aircraft would be flying fairly slow, with optimal speed being a trade-off between engine efficiency and the speed at which the wing can comfortable generate enough lift.
Going faster gets expensive quick.
So however efficient your propeller is at some (low) speed, as you get to faster and faster aircraft, 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, accelerating just bit with the propeller aircraft will be twice as expensive as with the jet.
That's also 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.
However, 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).
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 -- which is amazing) wants to take days to finish their intercontinental flight, and because propellers don't work so well at higher Mach numbers, jet engines (that is: Turbofans) are dominating commercial long-range flights. For high-efficiency flying over long distances, where speed is not that important, however, Propellers (mostly in the form of turboprops) are still popular. 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.
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.