Why are the top speeds for jet engines higher than for propellers?
The thrust of a propeller is proportional to the inverse of airspeed, while the thrust of a pure turbojet is roughly constant over airspeed in the subsonic region. This means that two airplanes with the same static thrust, one propeller-powered and the other jet-powered, will reach very different top speeds.

And, no, piston engines are more efficient.

A piston engine produces a constant torque $\tau$, independent of speed. This torque drives the propeller which produces work $W$ per unit of time on the air passing through it. This work per unit of time is power $P$ and proportional to the product of torque and propeller speed $\omega$, which is again constant over airspeed $v$. The power to propel the aircraft is the product of thrust and airspeed and equals engine power times propeller efficiency $\eta_{Prop}$. When airspeed goes up, thrust must go down proportionally for power to stay constant.
$$P = \tau\cdot\omega = T\cdot v\cdot\eta_{Prop}$$
$$\Rightarrow T \varpropto \frac{1}{v}$$

Turbojets, on the other hand, profit from flight speed because the intake pre-compresses the air when it slows down ahead of and in the intake. This pre-compression lifts the pressure level of the whole engine, so it sees an increased mass flow with increasing speed, producing higher thrust. This effect by itself would increase thrust in proportion with the square of flight speed, but the same effect which reduces the thrust of a propeller acts on a turbojet as well. This effect, however, is less pronounced because the jet accelerates less air to a higher speed, and both cancel each other, roughly.

Turbofans are more similar to propeller engines, so here the thrust goes down over airspeed, and more so for higher bypass ratios. Turboprops are even closer to piston-powered propellers, so their thrust drops even more with increasing speed. This means that the speed at which drag equals thrust drops when you move from turbojets to turbofans, and further to turboprops and is lowest for piston-powered propeller aircraft.