The Park Tool Handlebar Tape Installation guide suggests that the direction of wrapping can be either self tightening or prone to loosening. Its basic instructions make the tape self-tightening on the tops. The guide also describes how to start wrapping in a direction that makes the tape self-tightening in the drops, and then at the brake levers to switch to a direction that makes the tape self-tightening on the tops.
How much of a difference does the direction of wrapping make in practice? Is loosening of handlebar wrap a common problem? Are there any downsides to reversing the direction of handlebar tape at the brake levers, and if so, is it worth it?