Ask HN: For a greenfield public API which to use: REST, GraphQL, other? Why?

Definitely GraphQL. Github, Shopify, Yelp and many more are now using GraphQL as their primary public API.

You can use Introspected REST (https://introspected.rest) that allows you to fine-tune and balance between REST and GraphQL. No available libraries at the moment that can help you though so this could be a problem for your use case ;)

Depends on your use case.

GraphQL is designed for the use case of a client talking over a thin long pipe that needs to talk to many APIs. As in, it's designed for API clients that are smartphones.

And there are patent licensing issues with GraphQL.

It would help us answer the question if you told us more about your application.