Aims: We study the analogy between local luminous and ultraluminous infrared galaxies (U/LIRGs) and high-z massive star forming galaxies (SFGs) by comparing their basic Hα structural characteristics, such as size and luminosity surface density, in an homogeneous way (i.e. same tracer, size definition, and similar physical scales). Methods: We use integral field spectroscopy (IFS) based Hα emission maps for a representative sample of 54 local U/LIRGs (66 galaxies) observed with INTEGRAL/WHT and VIMOS/VLT. From this initial sample, we select 26 objects with similar Hα luminosities (L(Hα)) to those of massive (i.e. M⋆ ~ 1010 M&sun; or larger) SFGs at z ~ 2, and observed on similar physical scales. We then directly compare the sizes, and luminosity (and SFR) surface densities of these local and high-z samples. Results: The size of the Hα emitting region in the local U/LIRGs that we study has a wide range of values, with r1/2(Hα) from 0.2 kpc to 7 kpc. However, about two-thirds of local U/LIRGs with Lir > 1011.4 L&sun; have compact Hα emission (i.e. r1/2 < 2 kpc). The comparison sample of local U/LIRGs also contains a larger fraction (59%) of objects with compact Hα emission than the high-z sample (25%). This gives further support to the idea that for this luminosity range the size of the star forming region is a distinctive factor when comparing local and distant galaxies of similar SFRs. However, when using Hα as a tracer for both local and high-z samples, the differences are smaller than those reported using a variety of other tracers. In the L(Hα) - L(Hα) surface density (ΣHα) plane, most of the local U/LIRGs and high-z SF galaxies follow the same trend (i.e. higher luminosity for higher surface density) and cover a similar range, except for about 20-40% of local U/LIRGs, which have a higher ΣHα by a factor of about 10. This is considerably smaller than the factors of 1000 or more reported in similar planes (i.e. L(TIR) versus ΣTIR). Despite of the higher fraction of galaxies with compact Hα emission, a sizable group (about one-third) of local U/LIRGs are large (i.e. r1/2 > 2 kpc). These are systems that show evidence of pre-coalescence merger activity and are indistinguishable from the massive high-z SFGs galaxies in terms of their Hα sizes, and luminosity and SFR surface densities.