Quarter-wave monopole antennas actually use a ground plane to ‘complete’ the other half of the antenna - so it still operates as if it were a half-wave resonant antenna. This means that a quarter-wave antenna should occupy a smaller footprint on a circuit board. It’s for this reason that they’ve become the most popular form of embedded antenna.
If you take a 916MHz application, a full-wave antenna would need to be just shy of 330mm long. A quarter-wave version would only need to be 87.2mm long. Surface mounted antenna manufacturers can coil this up across multiple layers, but they still require a ground plane of this length to operate as the other radiator. Without a ground plane of one quarter of the wavelength, the antennas efficiency would be compromised and to an even greater degree when operating at lower frequencies.