  This paper is a sequel to our previous one (Kato et al.2015), which
calculated the luminosities and spectra of electron-type anti-neutrinos
($\bar{\nu}_e$'s) from the progenitors of core-collapse supernovae. Expecting
that a capability to detect electron-type neutrinos ($\nu_e$'s) will increase
dramatically with the emergence of liquid-argon detectors such as DUNE, we
broaden the scope in this study to include all-flavors of neutrinos emitted
from the pre-bounce phase. We pick up three progenitor models of an electron
capture supernova (ECSN) and iron-core collapse supernovae (FeCCSNe). We find
that the number luminosities reach $\sim10^{57} \mathrm{s^{-1}}$ and
$\sim10^{53} \mathrm{s^{-1}}$ at maximum for $\nu_e$ and $\bar{\nu}_e$,
respectively. We also estimate the numbers of detection events at terrestrial
neutrino detectors including DUNE, taking flavor oscillations into account and
assuming the distance to the progenitors to be 200 pc. It is demonstrated that
$\bar{\nu}_e$'s from the ECSN-progenitor will be undetected at almost all
detectors, whereas we will be able to observe $\gtrsim$15900 $\nu_e$'s at DUNE
for the inverted mass hierarchy. From the FeCCSN-progenitors, the number of
$\bar{\nu}_e$ events will be largest for JUNO, 200-900 $\bar{\nu}_e$'s,
depending on the mass hierarchy whereas the number of $\nu_e$ events at DUNE is
$\gtrsim$2100 for the inverted mass hierarchy. These results imply that the
detection of $\bar{\nu}_e$'s is useful to distinguish FeCCSN- from
ECSN-progenitors, while $\nu_e$'s will provide us with detailed information on
the collapse phase regardless of the type and mass of progenitor.
