  A systematic comparative study has been performed to better understand
DFT$+U$ (density functional theory + $U$) method. We examine the effect of
choosing different double counting and exchange-correlation functionals. The
calculated energy distribution and the Hund-$J$ dependence of potential profile
for representative configurations clearly show the different behaviors of each
DFT$+U$ formalism. In particular, adopting spin-dependent exchange-correlation
functionals likely leads to undesirable magnetic solution. Our analyses are
further highlighted by real material examples ranging from insulating oxides
(MnO and NiO) to metallic magnetic systems (SrRuO$_3$ and BaFe$_2$As$_2$). The
current work sheds new light on understanding DFT$+U$ and provides a guideline
to use the related methods.
