  Hubbard-corrected density-functional theory has proven to be successful in
addressing self-interaction errors in 3D magnetic materials. However, the
effectiveness of this approach for 2D magnetic materials has not been
extensively explored. Here, we use PBEsol+$\textit{U}$ and its extensions
PBEsol+$\textit{U}$+$\textit{V}$ to investigate the electronic, structural, and
vibrational properties of 2D antiferromagnetic FePS$_3$ and ferromagnetic
CrI$_3$, and compare the monolayers with their bulk counterparts. Hubbard
parameters (on-site $\textit{U}$ and inter-site $\textit{V}$) are computed
self-consistently using density-functional perturbation theory, thus avoiding
any empirical assumptions. We show that for FePS$_3$ the Hubbard corrections
are crucial in obtaining the experimentally observed insulating state with the
correct crystal symmetry, providing also vibrational frequencies in good
agreement with Raman experiments. For ferromagnetic CrI$_3$, we discuss how a
straightforward application of Hubbard corrections worsens the results and
introduces a spurious separation between spin-majority and minority conduction
bands. Promoting the Hubbard $\textit{U}$ to be a spin-resolved parameter -
that is, applying different (first-principles) values to the spin-up and
spin-down manifolds - recovers a more physical picture of the electronic bands
and delivers the best comparison with experiments.
