  We have carried out a comprehensive study of the intrinsic anomalous Hall
effect and spin Hall effect of several chiral antiferromagnetic compounds,
Mn$_3X$ ($X$ = Ge, Sn, Ga, Ir, Rh and Pt) by $ab~initio$ band structure and
Berry phase calculations. These studies reveal large and anisotropic values of
both the intrinsic anomalous Hall effect and spin Hall effect. The Mn$_3X$
materials exhibit a non-collinear antiferromagnetic order which, to avoid
geometrical frustration, forms planes of Mn moments that are arranged in a
Kagome-type lattice. With respect to these Kagome planes, we find that both the
anomalous Hall conductivity (AHC) and the spin Hall conductivity (SHC) are
quite anisotropic for any of these materials. Based on our calculations, we
propose how to maximize AHC and SHC for different materials. The band
structures and corresponding electron filling, that we show are essential to
determine the AHC and SHC, are compared for these different compounds. We point
out that Mn$_3$Ga shows a large SHC of about 600 $(\hbar/e)(\Omega\cdot
cm)^{-1}$. Our work provides insights into the realization of strong anomalous
Hall effects and spin Hall effects in chiral antiferromagetic materials.
