Buckle up, this is going to be a long comparison. Also, disclaimer, this was OpenAPI 2 I was looking at. I don't know what has changed in 3.
gRPC has its own dedicated specification language, and it's vastly superior to OpenAPI's JSON-based format. Being not JSON means you can include comments, which opens up the possibility of using .proto files as a one stop shop for completely documenting your protocols. And the gRPC code generators I played with even automatically incorporate these comments into the docstrings/javadoc/whatever of the generated client libraries, so people developing against gRPC APIs can even get the documentation in their editor's pop-up help.
Speaking of editor support, using its own language means that the IDEs I tried (vscode and intellij) offer much better editor assistance for .proto files than they do for OpenAPI specs. And it's just more concise and readable.
Finally, gRPC's proto files can import each other, which offers a great code reuse story. And it has a standard library for handling a lot of common patterns, which helps to eliminate a lot of uncertainty around things like, "How do we represent dates?"
Next is the code generation itself. gRPC spits out a library that you import, and it's a single library for both clients and servers. The server side stuff is typically an abstract class that you extend with your own implementation. I personally like that, since it helps keep a cleaner separation between "my code" and "generated code", and also makes life easier if you want to more than one service publishing some of the same APIs.
OpenAPI doesn't really have one way of doing it, because all of the code generators are community contributions (with varying levels of documentation), but the two most common ways to do it are to generate only client code, or to generate an entire server stub application whose implementation you fill in. Both are terrible, IMO. The first option means you need to manually ensure that the client and server remain 100% in sync, which eliminates one of the major potential benefits of using code generation in the first place. And the second makes API evolution more awkward, and renders the code generation all but useless for adding an API to an existing application.
gRPC's core team rules the code generation with an iron fist, which is both a pro and a con. On the upside, it means that things tend to behave very consistently, and all the official code generators meet a very high standard for maturity. On the downside, they tend to all be coded to the gRPC core team's standards, which are very enterprisey, and designed to try and be as consistent as possible across target languages. Meaning they tend to feel awkward and unidiomatic for every single target platform. For example, they place a high premium on minimizing breaking changes, which means that the Java edition, which has been around for a long time, continues to have a very Java 7 feel to it. That seems to rub most people (including me) the wrong way nowadays.
OpenAPI is much more, well, open. Some target platforms even have multiple code generators representing different people's vision for what the code should look like. Levels of completeness and documentation vary wildly. So, you're more likely to find a library that meets your own aesthetic standards, possibly at the cost of it being less-than-perfect from a technical perspective.
For my part, I came away with the impression that, at least if you're already using Envoy, anyway, gRPC + gRPC-web may be the least-fuss and most maintainable way to get a REST-y (no HATEOAS) API, too.
