Context. The kinematic characterization of different galaxy populations is a key observational input for distinguishing between different galaxy evolutionary scenarios because it helps to determine the number ratio of rotating disks to mergers at different cosmic epochs. Local (ultra) luminous infrared galaxies ((U)LIRGs) cover similar range of star formation rates (SFR) as normal high redshift (high-z), star-forming galaxies (SFGs). Therefore, their study offer a unique opportunity to study at high linear resolution and signal-to-noise (S/N) extreme star forming events and compare these events with those observed at high-z. Aims. Our goal is to analyze in detail the kinematics of the ionized gas as traced by the Hα emission of a large sample of 38 local (z < 0.1) (U)LIRG systems (50 individual galaxies). In this study, we apply kinematic criteria, which are able to characterize the evolutionary status of these systems, allowing us to derive the disk and merger ratio in such local systems. Methods. We obtained Very Large Telescope (VLT) VIMOS optical integral field spectroscopy (IFS) data of a sample of 38 (U)LIRGs. These systems are morphologically classified in four groups according to their dynamical phases: isolated disk, paired disk, ongoing merger, and post-coalescence merger. The first two are referred as "disk", while the second two are referred to as "merger". The "unweighted" and "weighted" kinemetry-based methods are used to kinematically classify our galaxies in disk and merger. The total kinematic asymmetry value K tot has been used to quantify the global kinematic asymmetry degree of the observed and simulated systems. Results. From the kinemetry-based analysis we are able classify our local (U)LIRGs in three distinct kinematic groups according to their total kinematic asymmetry values (K tot ) as derived when using the weighted (unweighted) method: (1) 25 out of 50 galaxies are kinematically classified as disk with a K tot ≤ 0.16 (0.14); (2) 9 out of 50 galaxies are kinematically classified as merger with a K tot ≥ 0.94 (0.66); (3) 16 out of 50 galaxies lie in the "transition region", in which disks and mergers coexist, with 0.16 (0.14) < K tot < 0.94 (0.66). The K tot frontier value that better classifies the highest numbers of disks and mergers, in agreement with their morphology, is K tot = 0.19 (∼0.15): using this value the fractions of "well-classified disks" (I disk ) vs. "well classified mergers" (I merger ) are, respectively, ∼80% vs. ∼100%. The same results are obtained if we only consider the isolated disks as "true disks". When we apply our criteria to the high-z simulated systems, a lower total kinematic asymmetry frontier value (K tot ∼ 0.16 (∼0.14)) is derived with respect to that found locally. The loss of angular resolution smears out the kinematic features, thus making objects to appear more kinematically regular (disky) than actually they are.