  We compare the Standard Model (SM) predictions for the differential branching
ratio of the rare $B\to K^*\nu\bar\nu$ decays using $B \to K^*$ form factors
obtained from holographic light-front QCD (hLFQCD) and Sum Rules (SR)
Distribution Amplitudes. For the total branching ratio, we predict
$\mathcal{BR}(\process)_{\rm hLFQCD}=(6.36^{+0.59}_{-0.74})\times 10^{-6}$ and
$\mathcal{BR}(\process)_{\rm SR}=(8.14^{+0.16}_{- 0.17})\times 10^{-6}$. More
interestingly, we find that the two model predictions for the differential
branching ratio are sufficiently different at low momentum transfer, so that
future measurements at Belle II may be able to discriminate between them. We
also confirm numerically that the $K^*$ longitudinal polarization fraction
$F_L$ has little sensitivity to the non-perturbative form factors and is thus
an excellent observable to probe New Physics signals. We predict
$F_L=0.40^{+0.02}_{-0.01}(0.41\pm 0.01)$ using hLFQCD (SR).
