1. Git, because of its source and momentum, is the more popular of the two. So when you are looking for code hosting that supports your tool bit bucket doesn't.
2. GitHub was first and seems to be better. Bit bucket has a reputation for being a cheap knock off of Git Hub for some reason.
3. I don't think you will find to many startup founders who really see a difference between the two price points, 10 bucks a month just isn't enough to worry about when bigger things like hardware costs and employee salaries dominate the list of costs.
The reason for this is very simple: We launched within months of each other, and we look very much alike (how many ways can you skin a DVCS hosting cat?) And then of course there was the whole pointing fingers/attempt to drag through the mud article, that was since removed.
Some people seem to like Gitorious.org which is apparently cheaper (free?)
Clickable: http://gitorious.org/