Aims. The aim of this work is twofold: first, to assess whether the population of elliptical galaxies in cluster at z~ 1.3 differs from the population in the field and whether their intrinsic structure depends on the environment where they belong; second, to constrain their properties 9 Gyr back in time through the study of their scaling relations. Methods. We compared a sample of 56 cluster elliptical galaxies selected from three clusters at 1.2 <z< 1.4 with elliptical galaxies selected at comparable redshift in the GOODS-South field (~30), in the COSMOS area (~180), and in the CANDELS fields (~220). To single out the environmental effects, we selected cluster and field elliptical galaxies according to their morphology. We compared physical and structural parameters of galaxies in the two environments and we derived the relationships between effective radius, surface brightness, stellar mass, and stellar mass density capital sigma Re within the effective radius and central mass density capital sigma sub(1 kpc), within 1 kpc radius. Results. We find that the structure and the properties of cluster elliptical galaxies do not differ from those in the field: they are characterized by the same structural parameters at fixed mass and they follow the same scaling relations. On the other hand, the population of field elliptical galaxies at z~ 1.3 shows a significant lack of massive (M sub(*)> 2 x 10 super(11)M sub(middot in circle)) and large (R sub(e)> 4-5 kpc) elliptical galaxies with respect to the cluster. Nonetheless, at M sub(*)< 2 x 10 super(11)M sub(middot in circle), the two populations are similar. The size-mass relation of cluster and field ellipticals at z~ 1.3 clearly defines two different regimes, above and below a transition mass m sub(t)Asymptotically = to 2-3 x 10 super(10)M sub(middot in circle): at lower masses the relation is nearly flat (R sub(e)is proportional to Mu sub(*) super(-0.1+ or -0.2)), the mean radius is nearly constant at ~1 kpc and, consequenly, capital sigma ReAsymptotically = to capital sigma sub(1 kpc) while, at larger masses, the relation is R sub(e)is proportional to Mu sub(*) super(0.64+ or -0.09). The transition mass marks the mass at which galaxies reach the maximum stellar mass density. Also the capital sigma sub(1 kpc)-mass relation follows two different regimes, above and below the transition mass ( capital sigma sub(1 kpc)is proportional to Mu sub(*) sub(1.07<mt) super(0.64>mt)) defining a transition mass density capital sigma sub(1 kpc)Asymptotically = to 2-3 x 10 super(3)M sub(middot in circle) pc super(-2). The effective stellar mass density capital sigma Re does not correlate with mass; dense/compact galaxies can be assembled over a wide mass regime, independently of the environment. The central stellar mass density, capital sigma sub(1 kpc), besides being correlated with the mass, is correlated to the age of the stellar population: the higher the central stellar mass density, the higher the mass, the older the age of the stellar population. Conclusions. While we found some evidence of environmental effects on the elliptical galaxies as a population, we did not find differences between the intrinsic properties of cluster and field elliptical galaxies at comparable redshift. The structure and the shaping of elliptical galaxies at z~ 1.3 do not depend on the environment. However, a dense environment seems to be more efficient in assembling high-mass large ellipticals, much rarer in the field at this redshift. The correlation found between the central stellar mass density and the age of the galaxies beside the mass shows the close connection of the central regions to the main phases of mass growth.