We will overview different formulations of superstring theory and 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). The equivalence is not a priori obvious, since while the physical bosonic sectors of the two formulations are the same in the conformal gauge, their fermionic sectors appear to be very different (first vs second derivative kinetic terms, presence vs absence of a fermionic gauge symmetry.