We present a detailed comparison of the CO (3-2) emitting molecular gas between a local sample of luminous infrared galaxies (U/LIRGs) and a high-redshift sample that comprises submm selected galaxies (SMGs), quasars, and Lyman Break Galaxies (LBGs). The U/LIRG sample consists of our recent CO (3-2) survey using the Submillimeter Array while the CO (3-2) data for the high-redshift population are obtained from the literature. We find that the L'(CO(3-2)) and L-FIR relation is correlated over five orders of magnitude, which suggests that the molecular gas traced in CO (3-2) emission is a robust tracer of dusty star formation activity. The near unity slope of 0.93 +/- 0.03 obtained from a fit to this relation suggests that the star formation efficiency is constant to within a factor of 2 across different types of galaxies residing in vastly different epochs. The CO (3-2) size measurements suggest that the molecular gas disks in local U/LIRGs (0.3-3.1 kpc) are much more compact than the SMGs (3-16 kpc), and that the size scales of SMGs are comparable to the nuclear separation (5-40 kpc) of the widely separated nuclei of U/LIRGs in our sample. We argue from these results that the SMGs studied here are predominantly intermediate stage mergers, and that the wider line widths arise from the violent merger of two massive gas-rich galaxies taking place deep in a massive halo potential.