  We demonstrate the equivalence between the worldsheet one-loop partition
functions computed near classical string solutions in the Green-Schwarz and in
the pure-spinor formulations of superstrings in AdS(5) x S(5). While their
bosonic sectors are the same in the conformal gauge, their fermionic sectors
superficially appear to be very different (first vs second derivative kinetic
terms, presence vs absence of fermionic gauge symmetry). Still, we show that
the quadratic fluctuation spectrum of sixteen fermionic modes of the
pure-spinor formulation is the same as in the Green-Schwarz superstring and the
contribution of the extra "massless" fermionic modes cancels against that of
the pure-spinor ghosts. We also provide evidence for a similar semiclassical
equivalence between the Green-Schwarz and the hybrid formulations of
superstrings in AdS(2) x S(2) x T(6) by studying several particular examples of
string solutions.
