hi EGYXee,
have you try to use Spatial Join (Analysis Tools) from ArcToolbox?
ArcToolbox --> Analysis Tools --> Overlay --> Spatial Join, from there you can choose Join Operation to : JOIN_ONE_TO_ONE (if only one small polygon in the big one),
don't worry, it doesn't need to have common field between target layer and source layer and
Match Option set to HAVE_THEIR_CENTER_IN