We use interferometric 12CO(1-0) observations to compare and contrast the extent, surface brightness profiles and kinematics of the molecular gas in CO-rich ATLAS3D early-type galaxies (ETGs) and spiral galaxies. We find that the molecular gas extent is smaller in absolute terms in ETGs than in late-type galaxies, but that the size distributions are similar once scaled by the galaxies optical/stellar characteristic scalelengths. Amongst ETGs, we find that the extent of the gas is independent of its kinematic misalignment (with respect to the stars), but does depend on the environment, with Virgo cluster ETGs having less extended molecular gas reservoirs, further emphasizing that cluster ETGs follow different evolutionary pathways from those in the field. Approximately half of ETGs have molecular gas surface brightness profiles that follow the stellar light profile. These systems often have relaxed gas out to large radii, suggesting they are unlikely to have had recent merger/accretion events. A third of the sample galaxies show molecular gas surface brightness profiles that fall off slower than the light, and sometimes show a truncation. These galaxies often have a low mass, and eitherhave disturbed molecular gas or are in the Virgo cluster, suggesting that recent mergers, ram pressure stripping and/or the presence of hot gas can compress/truncate the gas. The remaining galaxies have rings, or composite profiles, that we argue can be caused by the effects of bars. We investigated the kinematics of the molecular gas using position-velocity diagrams, and compared the observed kinematics with dynamical model predictions, and the observed stellar and ionized gas velocities. We confirm that the molecular gas reaches beyond the turnover of the circular velocity curve in~70 per cent of our CO-rich ATLAS3D ETGs, validating previous work on the CO Tully-Fisher relation. In general we find that in most galaxies the molecular gas is dynamically cold, and the observed CO rotation matches well model predictions of the circular velocity. In the galaxies with the largest molecular masses, dust obscuration and/or population gradients can cause model predictions of the circular velocity to disagree with observations of the molecular gas rotation; however, these effects are confined to the most star forming systems. Bars and non-equilibrium conditions can also make the gas deviate from circular orbits. In both these cases, one expects the model circular velocity to be higher than the observed CO velocity, in agreement with our observations. Molecular gas is a better direct tracer of the circular velocity than the ionized gas, justifying its use as a kinematic tracer for Tully-Fisher and similar analyses.