We present a direct comparison of the clustering properties of two redshift surveys covering a common volume of space: the recently completed IRAS Point Source Catalogue redshift survey (PSCz) containing 14500 galaxies with a limiting flux of 0.6 Jy at 60 microns, and the optical Stromlo-APM survey containing 1787 galaxies in a region of 4300 deg^2 in the southern Galactic cap. We use three methods to compare the clustering properties: the counts-in-cells comparison of Efstathiou (1995), the two-point cross correlation function, and the Tegmark (1998) `null-buster' test. We find that the Stromlo variances are systematically higher than those of PSCz, as expected due to the deficit of early-type galaxies in IRAS samples. However we find that the differences between the cell counts are consistent with a linear bias between the two surveys, with a relative bias parameter b_rel = b_Stromlo/b_PSCz ≈ 1.3 which appears approximately scale-independent. The correlation coefficient R between optical and IRAS densities on scales ∼ 20 Mpc/h is R > 0.72 at 95% c.l., placing limits on types of `stochastic bias' which affect optical and IRAS galaxies differently. ; Comment: Accepted for publication in MNRAS, 13 pages, 18 postscript figures