  We study the N\'eel to dimer transition driven by interlayer exchange
coupling in spin-S Heisenberg antiferromagnets on bilayer square and honeycomb
lattices for S=1/2, 1, 3/2. Using exact stochastic series expansion quantum
Monte Carlo (QMC) calculations, we find that the critical value of the
interlayer coupling, J_{\perp c}[S], increases with increasing S, with clear
evidence that the transition is in the O(3) universality class for all S. Using
bond operator mean field theory restricted to singlet and triplet states, we
find J_{\perp c}[S] ~ S(S+1), in qualitative accord with QMC, but the resulting
J_{\perp c} [S] is significantly smaller than the QMC value. For S=1/2,
incorporating triplet-triplet interactions within a variational approach yields
a critical interlayer coupling which agrees well with QMC. For higher spin, we
argue that it is crucial to account for the high energy quintet modes, and show
that including these within a perturbative scheme leads to reasonable agreement
with QMC results for S=1,3/2. We discuss the broad implications of our results
for systems such as the triangular lattice S=1 dimer compound Ba_3Mn_2O_8 and
the S=3/2 bilayer honeycomb material Bi_3Mn_4O_{12}(NO_{3}).
