Hi. Sorry to take so long to reply to your post but I have waiting for the Edinburgh weather to allow me to get out and acquire the data to answer your query about battery use. I have now compared both my Pro-Connect and my Pro-Connect S around a roughly 20 kilometre route around the North-West of Edinburgh. The weather conditions were broadly the same, and I've been round several times in the same direction using the same 18AH battery on each bike with the assistance level set to 'medium' continuously. With the Pro-Connect, battery elec use is roughly 6.25 Watthours per kilometre (10 Watthours per mile), whilst the PC-S elec use is roughly 8.75 Watthours per kilometre (14 Watthours per mile). So for the same distance the PC-S uses 40% more battery power.
I should point out, however, that on both bikes I've cycled at my normal comfortable cadence which results in an average speed on the PC-S about 10 to 15% higher than the PC, and a top speed about 20% higher. The 'fun factor' uplift is about 500%!