Take any well-known aggressive/dominant/predatory animal - wolves, big cats, bears, dragons, etc. Now say this animal were to have two heads, each equal in all capacities. What would realistically change from it's single-headed brethren?
I can imagine two possibilities:
1) Two heads would share (and split) the impulses of one body, reducing/sharing the aggression and impulses between them. For example, if a single-headed lion needs to eat a whole gazelle to feel satisfied, each head of a two-headed lion may think it only needs to eat half a gazelle. Two lion heads, each perceiving a fraction of the body's hunger, may be less driven to hunt.
2) Each head would get the full-blown drive of the body - in essence, a two-headed lion wants to hunt and eat two gazelles. This would surely make the multi-headed variety grow larger and become more dangerous, as it consumes and hunts twice as much with (arguably) twice as much drive.
Do either of these options seem more realistic over the other? Are there additional factors I'm not considering?