Oscars require space for them and their tank mates when they get too cramped or feel their tank mates are intruding on their territory in the tank they will make it known to all in and around the tank.
You may even find battle scars on your oscars from previous fights do not worry this will slow down as your oscars age,unless you have them in a small tank in which you will only see more of it. If one of your cuties is stoping the other from eating then I would in my experience recommend seperating them either by puting them in different tanks or by puting a barrier in. (which you can get from the fish store) Good luck with your oscars,all of you out there.
These photos clearly show bruises on both fish from disputes