  The thermodynamical ground-state properties and static response in both cold
atoms at or close to unitarity and neutron matter are determined using a
recently proposed Density Functional Theory (DFT) based on the s-wave
scattering length $a_s$, effective range $r_e$, and unitary gas limit. In cold
atoms, when the effective range may be neglected, we show that the pressure,
chemical potential, compressibility modulus and sound velocity obtained with
the DFT are compatible with experimental observations or exact theoretical
estimates. The static response in homogeneous infinite systems is also obtained
and a possible influence of the effective range on the response is analyzed.
The neutron matter differs from unitary gas due to the non infinite scattering
length and to a significant influence of effective range which affects all
thermodynamical quantities as well as the static response. In particular, we
show for neutron matter that the latter response recently obtained in
Auxiliary-Field Diffusion Monte-Carlo (AFDMC) can be qualitatively reproduced
when the p-wave contribution is added to the functional. Our study indicates
that the close similarity between the exact AFDMC static response and the free
gas response might stems from the compensation of the $a_s$ effect by the
effective range and p-wave contributions. We finally consider the dynamical
response of both atoms or neutron droplets in anisotropic traps. Assuming the
hydrodynamical regime and a polytropic equation of state, a reasonable
description of the radial and axial collective frequencies in cold atoms is
obtained. Following a similar strategy, we estimate the equivalent collective
frequencies of neutron drops in anisotropic traps.
