I've built neither but am about to build a pent shed for the main reason of ease of construction. However a pent does result in thicker joists due to the single straight span, I am wondering how effective ceiling storage of wood lengths maybe, and the design results in a high front eave which looks great but is an issue if you are not applying for PP due to max eave height under permitted development rights.
Issues with a mansard roof I could see, construction would be more challenging, you are making more eaves which if head height is limited would reduce usable space, covering the roof to be water tight would involve more seams. On the upside it would look nicer than a standard apex.
Fitz