Are graphql/apollo queries any more expensive than analogous queries using REST?

Is graphQL any harder on the DB than the analogous call using REST?

There are too many considerations here to properly answer your question.

The main focus of GraphQL is to help client side developers reduce the back & forth hard work of using fixed REST API endpoints to pull out the exact data a page requires. GraphQL permits requesting precisely the data required, no more no less. When they hit a query that’s not possible, the back-end guys have huge flexibility in how to add it to the suite of queryable sources the API publishes.

Meanwhile, the back end developers devising the GraphQL server API have complete control over how the various databases will be accessed.

As you can see, your question needs to be much more specific.