  We present new isochrone fits to the colour-magnitude diagrams of the
Galactic globular clusters NGC\,6362 and NGC\,6723. We utilize 22 and 26
photometric filters for NGC\,6362 and NGC\,6723, respectively, from the
ultraviolet to mid-infrared using data sets from {\it HST}, {\it Gaia}, unWISE,
and other photometric sources. We use models and isochrones from the Dartmouth
Stellar Evolution Database (DSED) and Bag of Stellar Tracks and Isochrones
(BaSTI) for $\alpha$-enhanced [$\alpha$/Fe]$=+0.4$ and different helium
abundances. The metallicities [Fe/H]$=-1.04\pm0.07$ and $-1.09\pm0.06$ are
derived from the red giant branch slopes in our fitting for NGC\,6362 and
NGC\,6723, respectively. They agree with spectroscopic estimates from the
literature. We find a differential reddening up to $\Delta E(B-V)=0.13$ mag in
the NGC\,6723 field due to the adjacent Corona Australis cloud complex. We
derive the following for NGC\,6362 and NGC\,6723, respectively: distances
$7.75\pm0.03\pm0.15$ (statistic and systematic error) and $8.15\pm0.04\pm0.15$
kpc; ages $12.0\pm0.1\pm0.8$ and $12.4\pm0.1\pm0.8$ Gyr; extinctions
$A_\mathrm{V}=0.19\pm0.04\pm0.06$ and $0.24\pm0.03\pm0.06$ mag; reddenings
$E(B-V)=0.056\pm0.01\pm0.02$ and $0.068\pm0.01\pm0.02$ mag. DSED provides
systematically lower [Fe/H] and higher reddenings than BaSTI. However, the
models agree in their relative estimates: NGC\,6723 is $0.44\pm0.04$ kpc
further, $0.5\pm0.1$ Gyr older, $\Delta E(B-V)=0.007\pm0.002$ more reddened,
and with $0.05\pm0.01$ dex lower [Fe/H] than NGC\,6362. The lower metallicity
and greater age of NGC\,6723 with respect to NGC\,6362 explain their horizontal
branch morphology difference. This confirms age as the second parameter for
these clusters. We provide lists of the cluster members from the {\it Gaia}
Data Release 3.
