A5 cell boundaries are geodesics. One more difference that I thought of is that HEALPix is generally not aligned with the continents (makes sense as it is mostly used for astrophysics), whereas the hilbert curve used to index A5 is aligned with the continental land masses: https://a5geo.org/examples/globe

As a result, when A5 is used as a spatial index, it will generally not have jumps in the cell index values when querying nearby locations on land