We study the properties of simulated high-redshift galaxies using cosmological N-body/gasdynamical runs from the OverWhelmingly Large Simulations (OWLS) project. The runs contrast several feedback implementations of varying effectiveness: from no feedback, to supernova-driven winds to powerful active galactic nucleus (AGN)-driven outflows. These different feedback models result in large variations in the abundance and structural properties of bright galaxies at z= 2. In agreement with earlier work, models with inefficient or no feedback lead to the formation of massive compact galaxies collecting a large fraction (upwards of 50 per cent) of all available baryons in each halo. Increasing the efficiency of feedback reduces the baryonic mass and increases the size of simulated galaxies. A model that includes supernova-driven gas outflows aided by the energetic output of AGNs reduces galaxy masses by roughly a factor of ˜10 compared with the no-feedback case. Other models give results that straddle these two extremes. Despite the large differences in galaxy formation efficiency, the net specific angular momentum of a galaxy is, on average, roughly half that of its surrounding halo, independent of halo mass (in the range probed) and of the feedback scheme. Feedback thus affects the baryonic mass of a galaxy much more severely than its spin. Feedback induces strong correlations between angular momentum content and galaxy mass that leave their imprint on galaxy scaling relations and morphologies. Encouragingly, we find that galaxy discs are common in moderate-feedback runs, making up typically ˜50 per cent of all galaxies at the centres of haloes with virial mass exceeding ˜1011 M⊙. The size, stellar masses and circular speeds of simulated galaxies formed in such runs have properties in between those of large star-forming discs and of compact early-type galaxies at z= 2. Once the detailed abundance and structural properties of these rare objects are well established, it may be possible to use them to gauge the overall efficacy of feedback in the formation of high-redshift galaxies.