Both of these cutting tools have convex blades and are often paired with rounded (concave) cutting boards. They are both used for rapid chopping and mincings, but the ulu is a more versatile knife as its single-handed design allows for scraping and more exact work than the mezzaluna. The mezzaluna (translates to "half moon") uses a two-handed design which means a larger blade is possible as is more leverage and thus cutting power but it's a less useful tool overall.