Different chemoselectivity of transition metals in catalytic hydrogenation
Unfortunately, this is extremely complicated and the topic of active research in both computational and inorganic chemistry and chemical engineering. There is no simple answer to your question. We can discuss various forces that go to determining chemoselectivity though.

1) Crystal structure: You said that you are primarily focused on bare metal catalysis, so I will restrict myself to those systems. Not all surfaces of even the same material behave the same. These are commonly described by Miller indices (1), which describe the surface by how a plane cuts through the material's unit cell. The reactivity and selectivity are heavily determined by the exact surface structure (think dangling bond sites, binding sites, multicenter reactivity, all of which are influenced by the surface atomic structure both local and in its immediate environs). Different materials will have different crystal structures based on both electronic effects (like how many valence electrons there are) and size effects (how big atoms are, although there is relatively less variation on this in the 2nd and 3rd rows).

2) Chemistry of binding sites: Some materials are more likely to bind molecules than others. The Pt-H bond is extremely strong, much more than a Pd-H bond (these trends down a period are often explained in terms of the diffuseness of the 5d orbitals vs 4d which lead to better overlap with the main group orbitals of hydrogen and other light elements). This leads to greater coverage of a Pt surface with hydride equivalents than a Pd surface (generally, caveats apply). On the other hand, Pd tends to bind oxygen atoms more strongly than Pt does (one can think about hard-soft acid base theory here to explain that, but the situation is probably more subtle and complicated than that). One can easily imagine a benzylic C-O oxygen bind to the Pd surface which holds the site for hydrogenation close the the surface until a hydride equivalent can diffuse over to react (hydrides on surfaces are quite mobile and diffusion is often quite rapid, of course, hydride diffusion rates are also strongly determined by surface structure and material properties (because almost nothing can be simple)). On the other hand, $\pi$-system can interact strongly with metal surface (especially of soft (again in the HSAB sense) metal). So, for Pt, the aromatic system is brought close to the surface, allowing hydrides to migrate over to it.

So we can hand-wavily discuss why Pd is more likely to hydrogenate benzylic C-O bonds and Pt is more likely to hydrogenate aromatic systems as we did above, but the nitty-gritty detail is quite complicated. This is a massive area of research. Inorganic chemistry is its own field not because everything is so similar, but because metals have hugely varying behavior. The fact that these are "all being transition metals" should NOT imply that their reactivity is similar in the slightest. Being in the same period as a transition metal tells you as much about being in the same period in the main group. C and O and N have totally different chemistry, as do Rh and Ru and Pd.

P.S. f orbitals do not figure into this.