I guess DDOS attacks - if we're checking the session ID on every request then that's a potential attack if you just make up uuids and throw them at the server.
But JWT's themselves are an attack vector, surely? If there's any mistake in the encryption (or any vulnerability in the libraries used) then this is a door open very wide indeed.
The beauty of session IDs is the simplicity of it - very few moving parts, so very few opportunities for mischief. JWTs seem to be the opposite: lots of moving parts, lots of opportunities.