The Passive Radiator Advantage
A passive radiator design affords a smaller, more stable, and lower distortion subwoofer design than does either the sealed or vented box.
(Background) The Vented Box
The traditional way to boost the bass output and/or extend the low frequency response of a sealed box speaker is to add a vent. Compared to the sealed box, the corner frequency moves lower, and output is higher. But this comes at the expense of going to a bigger box.
To keep vent velocity (and chuffing sounds) down, a larger vent diameter is desired. However, to get the tuning down low (as for a subwoofer), the vent must be long. So here we have the situation that calls for a big box, big vent, and long length. To get that length, often the vent undergoes one or two bends, i.e. a folded vent. Such a vent robs the needed larger internal volume even more.
Nevertheless, the vent diameter is limited, and the internal air velocity is still higher than we would like. Because the vent truly is a hole in the box, it is even possible for higher frequencies to literally leak out of the vent opening, and this midrange distortion is certainly audible.
Lastly, vents also exhibit self-resonance, also known as pipe resonance. These manifest as relatively high-value peak/dip combinations in the SPL response. So we get another unwanted source of distortion.
The Passive Radiator
A passive radiator is a good alternative to the vented box. Instead of the internal air vibrating inside a pipe, we have a large diaphragm vibrating back and forth. So the cone velocity (and hence the air velocity) can be kept quite low. No chuffing, no internal leakage, and no pipe resonances.
With the passive radiator design, woofer excursion is kept in check at the tune frequency. This is also where the passive radiator excursion is highest.
The passive radiator design works well in a box that is smaller than the vented design. All that has to be done is tune the passive radiator resonance lower to offset the higher tuning that comes from the smaller box. Fortunately this is much easier to do than for the vented box. We simply add weight to the backside of the passive radiator to achieve the low tune frequency for a subwoofer.
A downside to the passive radiator design is that its mass is much higher than the air inside a pipe, and hence the passive radiator vibration can transmit directly to the box in an action/reaction fashion. In other words, the heavy passive radiator vibrating violently at 20Hz will cause the subwoofer to literally wobble on the floor. Spikes and a heavy cabinet help.
But the best solution is to use two passive radiators, each mounted on opposing cabinet walls. Now the action/reaction effect is canceled out. In fact, the subwoofer is likely to hold still more than the vented box design. Whenever the subwoofer holds very still, the waveform truly is no longer compressed. Subjectively the bass sounds "tighter, articulate, and tuneful".