CBOR is a pretty good as a smaller / "better" JSON if you have a free hand choosing.
It has ambitions to replace ASN.1 / X.509 coding for certs, but I don't see it being used.
It is a bytewise binary coding, so you can't really write it by hand, whereas you definitely can expect to do that for JSON. However if you must send binary data, then it is a more natural fit, it will send it with a short header overhead rather than have to bloat it with base64.
It has ambitions to replace ASN.1 / X.509 coding for certs, but I don't see it being used.
It is a bytewise binary coding, so you can't really write it by hand, whereas you definitely can expect to do that for JSON. However if you must send binary data, then it is a more natural fit, it will send it with a short header overhead rather than have to bloat it with base64.