How would you convert a mesh/model into a voxel version?

How would you guys go about taking a model as an input, and outputting that model but voxelized with a variable resolution?

I've tried simply floodfilling and drawing cubes wherever a "voxel" contains a part which intersects its volume, but it doesn't look quite as nice as some of the tools I've seen which do this online. What am I missing?