The receivers for LiveATC and the like are frequently somewhat compromised in terms of quality and location. This can cause poor quality reception depending on the location and distance away of the transmitter.

The radios and antennas on both the aircraft and for ATC are not only of much higher quality but are also positioned as perfectly as possible so as to maximize Tx/Rx performance.

All that to say, the pilots and ATC nearly always experience more clear comms than the general public has access to.