I have 4 Bronze (or Green) Corydoras and 3 amano shrimp in my 10 gallon with 1 male betta. He doesn't mind them but the tank is heavily planted. If you're going to divide the tank, I'd go with shrimp. However you cannot be sure that one of the 3 bettas will be aggressive enough to kill/eat shrimp. With a divided tank, there is less room for any victim to escape a betta's jaws. Cory's MUST live in groups though, and they definitely need more space than a divided section of a 10 gallon tank...a 10 gallon itself is quite cramped for them as it is.
It largely depends on the betta...I had a CT that wouldn't let ghost shrimp or Corys live in peace so I had to return the cory's. The shrimp unfortunately all died.