I recently changed the leaking flat roof of the outbuildings and finally chose lean-to, because the beam is shorter, less materials and easier to work with, which means it’s cheaper. Gable end gives better lighting and ventilation of the attic, but higher fronton, more labor-intensive and requires additional grating. Check the height of the house, slope for water drainage, snow loads and if you need permission documentation, then it will be clear whether the difference is worth.