Messenger bag or handlebar basket?
Bikeshare bikes are beasts, and their geometry (long wheelbases, particularly) is such that I wouldn't think 15 pounds in front appreciably changes the steering. My concern -- the picture isn't clear on this point -- is whether the bag can be secured in place so that it doesn't slide out. My messenger bag sometimes gets loaded unevenly (books!), which could increase the chances it would fall out.

Heat is another consideration, especially given that hill. Messenger bags on your back hold in the heat! Hill might not be any harder that way, but it'll likely FEEL sweatier and more difficult.