I don't actually have a bottle cage on my bike at the moment, so it's always the left at present as I keep my water bottle in the stretchy mesh pocket on the left hand side of my backpack. I keep my cell phone and whatever else I want to be able to get to easily in the one on the right. I don't have a conscious reason for doing it this way around, but I've kept it consistent so that I can find what I'm looking for easily. Can't remember which hand I used when I did have a bottle cage - either/or I think.
Drink coffee and do stupid things faster with more energy.