I can imagine that it's stronger but what are the mechanisms in place that make this happen? And how much stronger?
Thinkable are three scenarios.
You use two identical permanent magnets. The attraction between them is stronger than that between a magnet and a magnetisable metal.
The reason for this is that the additional magnetic field of the magnetized metal comes from the alignment of the electrons or protons with their magnetic dipole moment to the applied magnetic field. These electrons have their own orientation equilibrium and the magnet cannot align the same amount of electrons in the metal as the magnet.
You use two permanent magnets of different strength. The attraction of the stronger magnet and the metal could be greater than between the two magnets.
The explanation is basically the same as in case 1. The orientation of additional electrons inside the smaller magnet could be less than the induces re-orientation of electrons in the metal.
The force of attraction between a permanent magnet and a metal is stronger than between two permanent magnets.
The crystalline metal structure is small in parts obtained by rapid cooling. The magnetic domains in such a metal developed poorly. This gives the probability of aligning many electrons in the metal, and this could end in a chain reaction of self-inductance; the metal transforms into a strong permanent magnet.
Normally the metal is not a compound with rare earths, unlike the permanent magnets. Then the electron configuration of the metal does not lead to such a strong magnetic field as with permanent magnets.