It depends a lot on your flying patterns.
If you generally fly paid J, there is very little to be gained from a *G card. A few airlines have nicer *G lounges than business class lounges. But with United introducing the Polaris Lounges, business class does have an advantage there.
The main benefit of a *G status comes when flying economy class. Fast track and lounges, and better/free seat selection comes with the status.
In order to reap benefits, you should start flying Star Alliance