1. Grant Types: ORY Hydra supports a wide range of grant types including authorization code, client credentials, refresh token, implicit, and resource owner password credentials, whereas OmniAuth primarily focuses on OAuth2 authorization code grant type.
2. Scalability: ORY Hydra is designed for high scalability, making it suitable for large enterprise applications handling a high volume of users and requests, while OmniAuth is more commonly used for smaller scale applications.
3. Customization: ORY Hydra provides extensive customization options for various aspects such as login, consent, and error pages, allowing developers to tailor the user experience, whereas OmniAuth is more limited in terms of customization capabilities.
4. Supported Protocols: ORY Hydra supports both OAuth2 and OpenID Connect protocols, making it versatile for various authentication and authorization scenarios, while OmniAuth focuses primarily on OAuth2 protocol.
5. Token Management: ORY Hydra offers robust token management features including token revocation and rotation, token introspection, and token persistence mechanisms, whereas OmniAuth is more focused on authentication middleware for various providers.
6. Community Support: ORY Hydra has a dedicated and active community providing ongoing support, updates, and additional resources, while OmniAuth has a smaller community with fewer resources available for troubleshooting and enhancement.

In Summary, ORY Hydra is feature-rich, scalable, and versatile with extensive customization options, while OmniAuth is more suitable for smaller scale applications with a focus on OAuth2 authorization code grant type.