We use the ages, masses and metallicities of the rich young star cluster systems in the nearby starburst galaxies NGC 3310 and NGC 6745 to derive their cluster formation histories and subsequent evolution. We further expand our analysis of the systematic uncertainties involved in the use of broad-band observations to derive these parameters by examining the effects of a priori assumptions on the individual cluster metallicities. The age (and metallicity) distributions of both the clusters in the circumnuclear ring in NGC 3310 and of those outside the ring are statistically indistinguishable, but there is a clear and significant excess of higher-mass clusters IN the ring compared to the non-ring cluster sample; it is likely that the physical conditions in the starburst ring may be conducive for the formation of higher-mass star clusters, on average, than in the relatively more quiescent environment of the main galactic disc. For the NGC 6745 cluster system we derive a median age of ~10 Myr. NGC 6745 contains a significant population of high-mass super star clusters, with masses in the range 6.5 <= log(M_cl/M_sun) <= 8.0. This detection supports the scenario that such objects form preferentially in the extreme environments of interacting galaxies. The age of the cluster populations in both NGC 3310 and NGC 6745 is significantly lower than their respective characteristic cluster disruption time-scales. This allows us to obtain an independent estimate of the INITIAL cluster mass function slope, alpha = 2.04(+- 0.23)(+0.13)(-0.43) for NGC 3310, and 1.96(+- 0.15)(+- 0.19) for NGC 6745, respectively, for masses M_cl >= 10^5 M_sun and M_cl >= 4 x 10^5 M_sun. These mass function slopes are consistent with those of other young star cluster systems in interacting and starburst galaxies.
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