H3 is a way of subdividing the (approximated) surface of a sphere into polygons that are (mostly) hexagons of approximately equal size (which requires smaller pentagons at what would can be envisioned as the corners of an icosahedron.)

The hexagon tiling honeycomb this refers to is a way of subdividing a particular 3D non-Euclidean space into polyhedra whose faces are hexagons.

They don’t really compare because they don’t address the same thing at all.

Not an expert, but I think it does not have pentagons because it is in a non-euclidian space. Might be wrong, just a guess.