  High to ultrahigh energy neutrino detectors can uniquely probe the properties
of dark matter $\chi$ by searching for the secondary products produced through
annihilation and/or decay processes. We evaluate the sensitivities to dark
matter thermally averaged annihilation cross section $\langle\sigma v\rangle$
and partial decay width into neutrinos $\Gamma_{\chi\rightarrow\nu\bar{\nu}}$
(in the mass scale $10^7 \leq m_\chi/{\rm GeV} \leq 10^{15}$) for next
generation observatories like POEMMA and GRAND. We show that in the range $
10^7 \leq m_\chi/{\rm GeV} \leq 10^{11}$, space-based Cherenkov detectors like
POEMMA have the advantage of full-sky coverage and rapid slewing, enabling an
optimized dark matter observation strategy focusing on the Galactic center. We
also show that ground-based radio detectors such as GRAND can achieve high
sensitivities and high duty cycles in radio quiet areas. We compare the
sensitivities of next generation neutrino experiments with existing constraints
from IceCube and updated 90\% C.L. upper limits on $\langle\sigma v\rangle$ and
$\Gamma_{\chi\rightarrow\nu\bar{\nu}}$ using results from the Pierre Auger
Collaboration and ANITA. We show that in the range $ 10^7 \leq m_\chi/{\rm GeV}
\leq 10^{11}$ POEMMA and GRAND10k will improve the neutrino sensitivity to
particle dark matter by factors of 2 to 10 over existing limits, whereas
GRAND200k will improve this sensitivity by two orders of magnitude. In the
range $10^{11} \leq m_\chi/{\rm GeV} \leq 10^{15}$, POEMMA's fluorescence
observation mode will achieve an unprecedented sensitivity to dark matter
properties. Finally, we highlight the importance of the uncertainties related
to the dark matter distribution in the Galactic halo, using the latest fit and
estimates of the Galactic parameters.
