REST APIs in API Gateway offer comprehensive features for creating, deploying, and managing APIs, including API keys, usage plans, and request validators. They are ideal for APIs that require end-to-end control and customization. On the other hand, HTTP APIs are a simplified version of REST APIs and focus on improving performance and reducing latency. They're up to 50% cheaper than REST APIs and offer built-in features like JWT authorizer support and automatic deployment. They're best suited for serverless workloads and building APIs for web applications.