The question should be "What is the advantage between a dual or single conversion receiver" as crystals are not classified as either. A crystal is just a block of quartz cut to resonate at a particular frequency. Now, dual conversion receivers require a crystal that is about 10.7 MHZ different than the transmitted signal, either more or less depending on the shift you want in the receiver. Single conversion crystals are 455 KHZ different in frequency from the transmitted signal. You usually need to also buy the crystals to match the brand of receiver, i.e. JR crystals for a JR receiver, a Futaba crystal for a Futaba receiver etc. Different design of the receiver oscillator circuits may require a different cut on the crystal, X, Y, Z or ??? depending on the electrical design of the oscillator in the receiver.