Keep in mind that the typical receiver antenna is not a whip, but a simple antenna system that consists of the feedline (typically a high-quality 50 ohm coax designed for microwave frequencies) and an antenna (typically, a coaxial dipole antenna).
On the receivers, you have the feedline exiting the case, extending to the tubular item in heat-shrink covering. This is the beginning of the coaxial dipole antenna (see a simple description here -- about 3/4 of the way down the page:
http://www.gonzales.com.au/joe/projects/videolink2/video_link_2.htm ).
The length of the feedline usually has no effect on antenna performance unless the lengths get very long (then signal loss in the feedline becomes a factor).
The actual antenna is another matter. As has been pointed out, the optimum length for the antenna elements is dictated by frequency and desired "directionality." Standard receiver antennas are designed to have a fairly uniform receive gain (how well the antenna receives) in all directions (there are exceptions, but let's stay with this, for now). You CAN increase the gain of the antenna, but ONLY at the expense of directionality. You can double the receive gain in some directions, but this makes the antenna ineffective in other directions (you can't get something for nothing). Certainly, this is not a desirable feature in an aircraft that can change its direction relative to the transmitter at any time.
Multi-rotors and other FPV platforms might use antennas that are optimized to increase gain in the downward direction (sacrificing gain in the upward direction), since there is no need to receive/transmit signals from/to the upward direction.
Think of it this way... Broadcast TV antennas for the home were highly directional -- they achieved greater gain in horizontal directions, but wouldn't do well at receiving signals from directly above. And you could make them even more directional to receive better in certain directions, but then they had to be more accurately pointed towards the transmitter.
To summarize, unless you know your aircraft will maintain a fairly fixed orientation to the transmitter, it's best to leave the receive antenna as omni-directional as possible.
(Of course, there is more complexity to this, especially if using multiple antennas, but that's another discussion).