Quasiballistic one-dimensional quantum wires are known to have a conductance of the order of 2e²/h, with small sample-to-sample fluctuations. We present a study of the transconductance G₁₂ of two Coulomb-coupled quasiballistic wires; i.e., we consider the Coulomb drag geometry. We show that the fluctuations in G₁₂ differ dramatically from those of the diagonal conductance G_ii: the fluctuations are large and can even exceed the mean value, thus implying a possible reversal of the induced drag current. We report extensive numerical simulations elucidating the fluctuations for both correlated and uncorrelated disorder. We also present analytic arguments, which fully account for the trends observed numerically.