Aims. In order to pinpoint the place of the (ultra-) luminous infrared galaxies ((U)LIRGs) in the local Universe, we examine the properties of a sample of 67 such nearby systems and compare them with those of 268 early- and 542 late-type, well studied, galaxies from the DustPedia database. Methods. We made use of multi-wavelength photometric data (from the ultra-violet to the sub-millimetre), culled from the literature, and the CIGALE spectral energy distribution fitting code to extract the physical parameters of each system. The median spectral energy distributions as well as the values of the derived parameters were compared to those of the local early- and late-type galaxies. In addition to that, (U)LIRGs were divided into seven classes, according to the merging stage of each system, and variations in the derived parameters were investigated. Results. (U)LIRGs occupy the ‘high-end’ on the dust mass, stellar mass, and star-formation rate (SFR) plane in the local Universe with median values of 5.2 × 10⁷ M_⊙, 6.3 × 10¹⁰ M_⊙, and 52 M_⊙ yr⁻¹, respectively. The median value of the dust temperature in (U)LIRGs is 32 K, which is higher compared to both the early-type (28 K) and the late-type (22 K) galaxies. The dust emission in PDR regions in (U)LIRGs is 11.7% of the total dust luminosity, which is significantly higher than early-type (1.6%) and late-type (5.2%) galaxies. Small differences in the derived parameters are seen for the seven merging classes of our sample of (U)LIRGs with the most evident one being on the SFR, where in systems in late merging stages (‘M3’ and ‘M4’) the median SFR reaches up to 99 M_⊙ yr⁻¹ compared to 26 M_⊙ yr⁻¹ for the isolated ones. In contrast to the local early- and late-type galaxies where the old stars are the dominant source of the stellar emission, the young stars in (U)LIRGs contribute with 64% of their luminosity to the total stellar luminosity. The fraction of the stellar luminosity absorbed by the dust is extremely high in (U)LIRGs (78%) compared to 7% and 25% in early- and late-type galaxies, respectively. The fraction of the stellar luminosity used to heat up the dust grains is very high in (U)LIRGs, for both stellar components (92% and 56% for the young and the old stellar populations, respectively) while 74% of the dust emission comes from the young stars.