The ryzen 7 serries will be great at streaming, frankly would go with 1700 and overclock it and save a good amount of money.
With that said i7-7700 will do a far better job at actually gaming. To most it is better to have better gameplay and be slightly slower streaming.
Now how well Ryzen games once games get optimized for it is still up in the air, so it is still a gamble at this point.