If users are on the same limited plans they're not using more bandwidth over any appreciable time scale.
In the real world, of course, people rarely download data endlessly and so the main difference is that a 4G user will use data at a higher rate for a shorter period of time since they're downloading the same YouTube video as the 3G user.
Since 4G takes considerably less time to establish connections than 3G, this trend is even more favorable to network operators since more phones can go from passive to active and back in any given time interval.