When it comes to stability there is a crucial handicap between ships and icebergs. The former have non-uniform mass, so it is possible for a ship's center of mass to be below its center of buoyancy. That's why ships have ballast - it lowers the center of mass relative to the center of buoyancy.

An iceberg is uniform, so its center of buoyancy is always below its center of mass. This makes its stability trickier, as it relies on changes in the shape of the buoyancy to follow the center of mass when disturbed.

A ship is a pendulum, an iceberg is an upright stick balanced on one's nose :)