Simply speaking, the difference between a single girder overhead crane and a double girder one is as we can see from their appearances, see below comparison picture:

Secondly, they are different from the lifting mechanism, normally there is a hoist(or two hoists) running one the single beam to carry and lift load; then double girder crane has two types: QD and LH, trolley are running on the double girder for both types, nevertheless, QD trolley uses a winch as lifting mechanism while LH trolley uses hoists, see below comparison picture:

Thirdly, they are different in applications: Single girder overhead crane is normally used in light duty load (20ton) lifting and short operation time (6 hours), double girder normally used in heavy duty load(above 20 ton) and long time operation(8 hours or above) thanks to its strong stability.

Last difference is very sensitive---the price, we can get the answer from above double girder is more expensive then single girder one due to different structure and mechanisms.