In theory a half-wave antenna would be a better performer for more distant signals, given its radiation pattern, although that is more important for transmitting than receiving and given the strength of ADSB signals, the difference would probably be negligible.
Half-wave antennas also less reliant on ground, although we shouldn't go as far as to declare them to be ground independent, as some manufacturers claim.
One other significant difference though is the feedpoint impedance. The quarter wave is a relatively low impedance feedpoint device, hence our ability to fed it happily through 50 ohm coax cable. Not so the half-wave. It is a high impedance feedpoint device and should really be connected to the coax via an impedance matching circuit, such as a parallel combination of a coil and a capacitor, tuned to the frequency of operation. That tuned circuit, often called a tank, has a low impedance at the bottom of the pair but a high impedance at its top. That characteristic of a parallel tuned circuit makes it easy to connect the antenna to the top and the 50 ohm coax to the bottom.
in terms of tuning the antenna to resonance, 4mm at 1090MHz is a significant difference in length.