  We have combined observations of the Antennae galaxies from the radio
interferometer ALMA (Atacama Large Millimeter/submillimeter Array) and from the
optical interferometer GH$\alpha$FaS (Galaxy H$\alpha$ Fabry-Perot System). The
two sets of observations have comparable angular and spectral resolutions,
enabling us to identify 142 giant molecular clouds (GMCs) and 303 HII regions.
We have measured, and compared, their basic physical properties (radius,
velocity dispersion, luminosity). For the HII regions, we find two physical
regimes, one for masses $>10^{5.4} \mathrm{M_{\odot}}$ of ionized gas, where
the gas density increases with gas mass, the other for masses $<10^{5.4}
\mathrm{M_{\odot}}$ of ionized gas, where the gas density decreases with gas
mass. For the GMCs, we find, in contrast to previous studies in other galaxies
over a generally lower mass range of clouds, that the gas surface density
increases with the radius, hinting at two regimes for these clouds if we
consider both sources of data. We also find that the GMC mass function has a
break at $10^{6.7}\mathrm{M_{\odot}}$. Using the velocity dispersion
measurements, we claim that the difference between the regimes is the nature of
the dominant binding force. For the regions in the lower mass range, the
dominant force is the external pressure, while in the higher mass range it is
the internal gravity of the clouds. In the regime where gravity is dominant,
the star formation rate, derived from the dust-corrected H$\alpha$ luminosity,
increases super-linearly with the velocity dispersion, and the gas density
increases with the gas mass.
