Volume of cycled filter media is roughly per supported ammonia-secreting fish, in other words if the media was supporting 4 fish in the older smaller aquarium, it might support 4 fish in the newer bigger aquarium because (if it has had time) it will have topped out at a bacterial population that supports 4 fish plus whatever other debris created ammonia it is receiving as the filter water passes over it. Volume of tank water should not be a big facter. However, disruption and change can affect the bacterial population, so one might expect, say in this example that maybe supporting 2 or 3 fish on the other end of the transfer initially would be a safer chance to take.
If you have to leave the smaller aquarium running, I've read on TFF the recommendation that you divide the bio-filter media and move one third to the new filter, somehow adding it physically in the the new media of the new filter. If you want to read more try some searches on backtotropical, as he wrote a nice bit in a recent thread (I think over in new to the hobby forum.)
Hope these thoughts make sense and help a little, waterdrop