They keep you dry, so long as the wind is favorable. If you have wind that doesn't shift, you're fine, but basically you have at least one side open- you can't do much if the weather changes without building a second shelter. A good shelter works no matter the wind direction.

As for keeping you warm, those open sides and living space are the kicker. Leantos reflect heat from a fire fairly well, but keeping it in if there is no fire is something they don't do so well.

The sole advantage of a lean to is it is easy to remember how to make, and require relatively few materials to make a basic windbreak and reflector. And most manuals will the proceed to the debris shelter, and point out that it works much more efficently.

A wickup (debris shelter) works a lot better, becuase while it doesn't have the space to move in, your body heat can heat it, and the heat of the fire can heat it efficently and effectively. That also means you can have a smaller fire that requires less fuel to keep you warm.