Using B, R and Hα images of roughly equal-sized samples of low surface brightness (LSB) and high surface brightness (HSB) galaxies (~40 galaxies apiece), we have explored the dependence of HII region properties on local and global disc surface brightness. We have done this by constructing co-added HII region luminosity functions (LFs) according to local and central disc surface brightness and fitting Schechter functions to these LFs. The results show that the shape of the HII region LF within LSB galaxies does not change noticeably as different limiting (i.e. μ > μlim) local surface brightness values are used. However, the LFs for HSB galaxies have larger values of L* and are less steep at the faint-end than those of LSB galaxies for limiting B-band local surface brightness values as faint as μB,lim ~= 23- 24. Both the LFs and the data for individual HII regions show that luminous (L > 1039ergs-1) HII regions are much more common within HSB discs than within LSB discs, implying that the newly formed star clusters are also larger. Taking this into account along with the results of Monte Carlo simulations, the shapes of the LFs imply that the regions within LSB discs and those within the LSB areas of HSB discs are relatively old (~5Myr) while the regions within HSB discs for μB <~ 24 are significantly younger (<1Myr). Since the majority of the LSB galaxies do not have noticeable spiral arms and the majority of the HSB galaxies do, this may indicate a transition within HSB discs from spiral arm-driven star formation to a more locally driven, possibly sporadic form of star formation at μB ~ 24, a transition that does not appear to occur within LSB discs.