A dipole antenna is linearly polarised, which means it radiates most of its energy in one 'plane' relative to the antenna. For maximum efficiency, the transmit and receive antenna should be orientated such that their plane of radiation is the same, or very close to.
It is important to note that as the aircraft flies around, the orientation of the antenna changes with the aircraft. The reason a vertical orientation is recommended is that aircraft - particularly multirotors - generally1 fly with one side 'up'; therefore, for whichever direction the aircraft is travelling the antenna is still vertical (or, mostly so) compared with the transmitter.
With a horizontally orientated antenna, when the aircraft turns through 90° relative to the transmitter, the antenna is now 90° out of alignment to the transmitter; it may help to think of/visualise this as "North/South" and "East/West", and the loss of signal will be comparable to vertical vs. horizontal as the angle difference is the same. Some receivers have multiple antennas and recommend orientating them at 90° to each other to mitigate this scenario.
What you may consider, if your transmitter permits it, is to have the antenna at a 45° angle as a compromise for signal strength. Most drones have a built-in lost comms failsafe so a loss of signal should not be a huge concern; for a fixed-wing model aircraft, I would be more concerned about matching antenna orientations.
 The main exceptions probably being stunt aircraft