Messenger bag or handlebar basket? Fairly straightforward question the answer to which I presume depends upon ride distance, terrain, bike type, and bag weight, but I'm hoping there's a rule of thumb that generally applies to all scenarios.

This question dawned on me as I was mounting a Citi Bike last night:

Should I keep my messenger bag (weighing about 15 lbs.) strapped to my back, or should I secure it in the "protective rack" attached to the handlebars?

My thinking at the time: The bag would fit perfectly, but it would weigh down the front of the bike and make it more difficult to steer. 

I opted to keep the bag strapped to my back, but this decision was based on 100% conjecture. I have little to no experience riding with belongings in a handlebar basket. On the other hand, I very often ride with a heavy messenger bag. It's habit at this point, and maybe a bad one.

The ride proved uneventful, though I can report that it isn't exactly easy riding the incline of the Williamsburg Bridge while wearing a full messenger bag on a 45 lbs Citi Bike. Would the ride have been any easier if I had put my bag in the 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.