The values in the EPC seem more random.

Granted, but there are also nowhere near as many of them. Besides, fermion mass increases to the right, same as in the PT; charge depends only on the row; and spin is 1/2 for all fermions and 1 for all bosons. This is not very complicated.

I would also suggest that the seeming randomness is a sign you're getting closer to the genuinely fundamental stuff: The order in the periodic table is due to (using loose language) repeated interactions of only a few underlying rules - basically just combinations of up and down quarks, with electrons, and electromagnetic interactions only.

For me, it's mainly a matter of the properties shown on the chart being more abstract and not knowing what observations they would map to.

Nu, mass and charge are hardly abstract for someone who has done basic physics; that leaves spin, which just maps to the observation that a beam of electrons in a magnetic field will split into two. (Although admittedly things then get a bit counter-intuitive if you put one of the split beams through a further magnetic field at a different angle, but that's more the usual QM confusion.)