The original tool you show is modeled after Rolex's 1009 tool, which is used to remove non-rotating bezels from their oyster cases (they friction around either the acrylic crystal if a vintage model, or a tall crystal gasket if a sapphire one, holding the crystal/gasket onto the crystal seat inside). Entirely different type of friction involved, and they make different tools to remove their rotating bezels. I'd not recommend using that type of tool for removing rotating bezels on pretty much any brand, as it is a very controlled way to leave marks and possibly distort the bezel or the case. It's just not meant for that specific task.