We present a comparative study of the molecular gas in two galaxies from the Legacy ExtraGalactic UV Survey (LEGUS) sample: barred spiral NGC 1313 and flocculent spiral NGC 7793. These two galaxies have similar masses, metallicities, and star formation rates, but NGC 1313 is forming significantly more massive star clusters than NGC 7793, especially young massive clusters (<10 Myr, >10⁴M_⊙). Using Atacama Large Millimeter/submillimeter Array (ALMA) CO(2–1) observations of the two galaxies with the same sensitivity and resolution (13 pc), we directly compare the molecular gas in these two similar galaxies to determine the physical conditions responsible for their large disparity in cluster formation. By fitting size–line width relations for the clouds in each galaxy, we find that NGC 1313 has a higher intercept than NGC 7793, implying that its clouds have higher kinetic energies at a given size scale. NGC 1313 also has more clouds near virial equilibrium than NGC 7793, which may be connected to its higher rate of massive cluster formation. However, these virially bound clouds do not show a stronger correlation with young clusters than with the general cloud population. We find surprisingly small differences between the distributions of molecular cloud populations in the two galaxies, though the largest of those differences is that NGC 1313 has higher surface densities and lower freefall times.