Did you leave any old filter media in the old filter? If not, then you may throw the 10 gallon into a cycle. If the old cartridge is sitting in the new tank with no filter/oxygen/airstone then a lot, if not all, of the beneficial bacteria will start dying. Don't forget to throw some flake food in the tank so the bb's can feed on it... starving bacteria = dead bacteria.
There's a sponge and a cartridge in the old tank. I've changed that cartridge 5 or 6 times this year with no problems. Problably due to the fact that theres just a guppy, a pleco, and a shrimp in there... Along with a lot of generic plant. This should basically be the same. The several month old cartridge is now floating in the new tank with the new filter running.