It is to my understanding that there are only specification differences between the two models listed in the title. If I wanted to restore a backup from a 4140 to a 4120 appliance, then will I run into any problems? Is this possible in the first place?
What's your goal? To move to a new chassis?
There is a configuration export/import - is that what you're talking about? It has some guidelines and limitations but doesn't say the hardware model needs to be exactly the same.
Still, I would ask cisco TAC directly or even have your SE lab it up in Customer POC lab or such.
Most of the interesting bits are in the logical device (FTD or ASA). Those are not backed up by the export and need to be handled in their respective manager (FMC for FTD or cli/ASDM/CSM/CDO etc. for ASA).