Aims: We investigate the physical and morphological properties of Lyman break galaxies (LBGs) at redshift ~2.5 to ~3.5, to determine if and how they depend on the nature and strength of the Lyalpha emission. Methods: We selected U-dropout galaxies from the z-detected GOODS-MUSIC catalog by adapting the classical Lyman break criteria on the GOODS filter set. We kept only those galaxies with spectroscopic confirmation, mainly from VIMOS and FORS public observations. Using the full multi-wavelength 14-bands information (U to IRAC), we determined the physical properties of the galaxies through a standard spectral energy distribution fitting procedure with the updated Charlot & Bruzual (2009) templates. We also added other relevant observations of the GOODS field, i.e. the 24 mum observations from Spitzer/MIPS and the 2 MSec Chandra X-ray observations. Finally, using non parametric diagnostics (Gini, Concentration, Asymmetry, M20 and ellipticity), we characterized the rest-frame UV morphologies of the galaxies. We then analyzed how these physical and morphological properties correlate with the presence of the Lyalpha emission line in the optical spectra. Results: We find that unlike at higher redshift, the dependence of physical properties on the Lyalpha line is milder: galaxies without Lyalpha in emission tend to be more massive and dustier than the rest of the sample, but all other parameters, ages, star formation rates (SFR), X-ray emission and UV morphology do not depend strongly on the presence of the Lyalpha emission. A simple scenario where all LBGs have intrinsically high Lyalpha emission, but where the dust and neutral hydrogen content (which shapes the final appearance of the Lyalpha) depend on the mass of the galaxies, is able to reproduce the majority of the observed properties at z˜3. Some modification might be needed to account for the observed evolution of these properties with cosmic epoch, which is also discussed.