Ive seen tempermental males chase corys, but never hurt them. That only 2 of my bettas did that out of many. They were mean little suckers to begin with.
Females seem to get along with them very well.
I have 5 female Bettas(with plenty of places for each to call their own) and 3 albino corys in a 15 gallon and they all get along great. Closing in a year now theyre all been together.
I feed my Corys Wardley Shrimp Pellet Formula and they DEVOUR them. Trouble is the Bettas love them too. Ive never seen a Betta hurt of Cory to get to the food. They all eat peacefully. But my Bettas were getting pretty fat for awhile there because theyd eat their food and them join the corys on the pellets.
So I usually drop in the Corys a pellet and keep the Bettas preoccupied, feeding them slowly and hovering near the top for while so the Corys can eat in peace.
Also I always keep my Corys in groups of 3s or more. Theyre much happier with a few of them in there.