The biggest difference in a Green vs Ordinary Japan Rail Pass is the space in each car / wagon. The Green cars are less seats per row and per wagon, giving a more quiet and better travel experience. The seats are wider and with more alternatives like heating, reclining seats, foot rests etc.
And when it comes to amenities, they will come with either hot or cold oshibori after each stop, priority on the snack and food carts, and some rides offer free snacks, candy, icecream and dricks. It all varies on the train however, and the free snacks and drinks are usually on longer train rides.
The Green Pass is not worth to get for the amenities alone, but a great alternative for travllers who wish to travel with a better seats and less crowded wagons.
With kind regards, Jonathan H.