High-resolution electron spectroscopy is used to explore the role played by molecular symmetry in determining the morphology of the energy spectra of electrons ejected when N2 and O2 are irradiated by intense laser fields. In O2, the low-energy part of the electron spectrum is curtailed due to the destructive interference brought about by the antibonding nature of the O2 valence orbital. The high-energy tail of the spectrum is also suppressed by virtue of electron rescattering being of little consequence in O2. In contrast, in N2, which has a bonding valence orbital, the electron dynamics follow the pattern that has been established for atomic ionization in strong optical fields.