  We present a comparative study of X-ray and IR AGNs at $z\approx2$ to
highlight the important AGN selection effects on the distributions of host
galaxy properties. Compared with non-AGN star-forming galaxies (SFGs) on the
main sequence, X-ray AGNs have similar median star formation (SF) properties,
but their incidence (q$_{\rm{AGN}}$) is higher among galaxies with either
enhanced or suppressed SF, and among galaxies with larger stellar mass surface
density, regardless if it is measured within half-light radius ($\Sigma_e$) or
central 1kpc ($\Sigma_{\rm{1kpc}}$). Unlike X-ray AGNs, IR AGNs are less
massive, and have enhanced SF and similar distributions of colors, $\Sigma_e$
and $\Sigma_{\rm{1kpc}}$ relative to non-AGN SFGs. Given that $\Sigma_e$ and
$\Sigma_{\rm{1kpc}}$ strongly correlate with M$_*$, we introduce the fractional
mass within central 1kpc ($\rm{\frac{M_{1kpc}}{M_*}}$), which only weakly
depends on M$_*$, to quantify galaxy compactness. Both AGN populations have
similar $\rm{\frac{M_{1kpc}}{M_*}}$ distributions compared to non-AGN SFGs'.
While q$_{\rm{AGN}}$ increases with $\Sigma_e$ and $\Sigma_{\rm{1kpc}}$, it
remains constant with $\rm{\frac{M_{1kpc}}{M_*}}$, indicating that the trend of
increasing q$_{\rm{AGN}}$ with $\rm{\Sigma}$ is driven by M$_*$ more than
morphology. While our findings are not in conflict with the scenario of AGN
quenching, they do not imply it either, because the incidence of AGNs hosted in
transitional galaxies depends crucially on AGN selections. Additionally,
despite the relatively large uncertainty of AGN bolometric luminosities, their
very weak correlation, if any, with SF activities, regardless of AGN
selections, also argues against a direct causal link between the presences of
AGNs and the quenching of massive galaxies at $z\sim2$.
