Bettas are mostly and pretty much carnivores, but will pretty much eat anything you give 'em. One time years ago, I gave my Oscar and betta a piece of McDonald's hamburger lol!!!
You can also give Corys shrimp pellets as well. Bettas will eat those too. Bettas are essentially kinda like goats: I soak and soften shrimp pellets in Seachem's Garlic Guard and my Corys go nuts for 'em! As well as the betta. And yes, bettas can sometimes be finicky anyway, but eventually you'll discover his fave food in the long run. The key is to try different foods. Especially the meaty ones.