  PtTe$_2$ and PdTe$_2$ are among the first transition metal dichalcogenides
that were predicted to host type-II Dirac fermions, exotic particles prohibited
in free space. These materials are layered and air-stable, which makes them top
candidates for technological applications that take advantage of their
anisotropic magnetotransport properties. Here, we provide a detailed
characterization of the electronic structure of PtTe$_2$ and PdTe$_2$ using
Angle Resolved Photoemission Spectroscopy (ARPES) and Density Functional Theory
(DFT) calculations, unveiling a new three-dimensional dispersion in these
materials. Through the use of circularly polarized light, we report a different
behavior of such dispersion in PdTe$_2$ compared to PtTe$_2$, that we relate to
a symmetry analysis of the dipole matrix element. Such analysis reveals a link
between the observed circular dichroism and the different momentum-dependent
terms in the dispersion of these two compounds, despite their close similarity
in crystal structure. Additionally, our data shows a clear difference in the
circular dichroic signal for the type-II Dirac cones characteristic of these
materials, compared to their topologically protected surface states. Our work
provides a useful reference for the ARPES characterization of other transition
metal dichalcogenides with topological properties and illustrates the use of
circular dichroism as a guide to identify the topological character of two
otherwise equivalent band dispersions, and to recognize different attributes in
the band structure of similar materials.
