Normally on a modded console, your SD Card have a EmuNAND, that EmuNAND is DEPENDANT of the console because the encryption keys, so you can not just shove the sd card on another console.
If you want the same games you need to install them on the new console, if you like to transfer your savegames, you need backup it on the source console (I do recommend using JKSV) and then import them on the new console.