Companding schemes are widely employed to reduce the peak-to-average-power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. This paper considers the classes of linear and nonlinear companding schemes and derives a sufficient condition under which the bit error rate (BER) performance of one is superior to that of the other. The high PAPR of the OFDM signal drives the transmitter's power amplifier into its nonlinear region, thus causing nonlinear distortions. In the literature, signal companding is one of the widely used techniques for PAPR reduction. Furthermore, it has been claimed, based on simulation results, that linear companding performs better, in terms of BER, than nonlinear companding for an optimized set of companding parameters. In this paper, we derive sufficient conditions under which these claims are valid. The conditions derived also show that, in practice, nonlinear companding transforms perform better than linear companding transform. Our theoretical analysis is supported by simulation results.