We have conducted deep photometric searches for substellar members of the Praesepe (0.5-1 Gyr) and σ Orionis (3 Myr) star clusters using the Sloan i' and z' broad-band filters, with the 3.5-m and the 5-m Hale telescopes on the Calar Alto and Palomar Observatories. The total area surveyed was 1177 arcmin2 and 1122 arcmin2 towards the central regions of Praesepe and σ Orionis, respectively. The 5-σ detection limit of our survey is measured at i' = 24.5 and z' = 24 mag, which according to state-of-the-art evolutionary models corresponds to masses of 50-55 M_Jup (Praesepe) and 6 M_Jup (σ Orionis), i.e., well within the substellar regime. Besides recovering previously known cluster members reported in the literature, we have identified new photometric candidates in both clusters whose masses expand the full range covered by our study. In σ Orionis, follow-up near-infrared photometry has allowed us to confirm the likely cluster membership of three newly discovered planetary-mass objects. The substellar mass function of σ Orionis, which is complete from the star-brown dwarf borderline down to 7 M_Jup, rises smoothly with a slope of α = 0.6 +0.5-0.1 (dN/dM ˜ M-α). One of the faintest Praesepe candidates for which we have obtained follow-up near-infrared JHKs photometry closely fits the expected optical and infrared photometric sequence of the cluster. From its colors, we have estimated its spectral type to be between L4 and L6. If confirmed as a true Praesepe member, it would become the first L-type brown dwarf (50-60 M_Jup) identified in an intermediate-age star cluster. Our derivation of the Praesepe mass function, which is based on state-of-the-art evolutionary models, depends strongly on the cluster age. For the youngest possible ages (500-700 Myr), our results suggest that there is a deficit of Praesepe brown dwarfs in the central regions of the cluster, while the similarity between the Praesepe and σ Orionis mass functions increases qualitatively for models older than 800 Myr.