We use high-resolution Hydro+N-Body cosmological simulations to compare the assembly and evolution of a small field dwarf (stellar mass ∼106−7M⊙, total mass 1010M⊙) in Λ-dominated cold dark matter (CDM) and 2keV warm dark matter (WDM) cosmologies. We find that star formation (SF) in the WDM model is reduced and delayed by 1-2Gyr relative to the CDM model, independently of the details of SF and feedback. Independent of the dark matter (DM) model, but proportionally to the SF efficiency, gas outflows lower the central mass density through ‘dynamical heating', such that all realizations have circular velocities <20 km s−1 at 500pc, in agreement with local kinematic constraints. As a result of dynamical heating, older stars are less centrally concentrated than younger stars, similar to stellar population gradients observed in nearby dwarf galaxies. Introducing an important diagnostic of SF and feedback models, we translate our simulations into artificial colour-magnitude diagrams and star formation histories (SFHs) in order to directly compare to available observations. The simulated galaxies formed most of their stars in many ∼10Myr long bursts. The CDM galaxy has a global SFH, H i abundance and Fe/H and alpha-elements distribution well matched to current observations of dwarf galaxies. These results highlight the importance of directly including ‘baryon physics' in simulations when (1) comparing predictions of galaxy formation models with the kinematics and number density of local dwarf galaxies and (2) differentiating between CDM and non-standard models with different DM or power spectr