I've definitely heard of someone having the "gift of the gab", meaning they speak convincingly (I think I've only heard it used to describe sales people though).
"gift of the gab" can be positive, meaning a confident successful communicator (and sometimes socialiser) though tone of voice can turn it negative, meaning someone who successfully communicates bullshit (got instance in a marketing context).
Gobby is pretty much always negative, meaning loud, never shutting up, often also implying overly opinionated and/or obnoxious.
