  Recently discovered (CaFe$_{1-x}$Pt$_x$As)$_{10}$Pt$_3$As$_8$ and
(CaFeAs)$_{10}$Pt$_{4-y}$As$_8$ superconductors are very similar materials
having the same elemental composition and structurally similar superconducting
FeAs slabs. Yet the maximal critical temperature achieved by changing Pt
concentration is approximately twice higher in the latter. Using angle-resolved
photoemission spectroscopy(ARPES) we compare the electronic structure of their
optimally doped compounds and find drastic differences. Our results highlight
the sensitivity of critical temperature to the details of fermiology and point
to the decisive role of band-edge singularities in the mechanism of high-$T_c$
superconductivity.
