  We use high resolution Hydro$+$N-Body cosmological simulations to compare the
assembly and evolution of a small field dwarf (stellar mass ~ 10$^{6-7}$
M$\odot$, total mass 10$^{10}$ M$\odot$ in $\Lambda$ dominated CDM and 2keV WDM
cosmologies. We find that star formation (SF) in the WDM model is reduced and
delayed by 1-2 Gyr relative to the CDM model, independently of the details of
SF and feedback. Independent of the 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 $<$ 20kms at
500$~$pc, 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 color-magnitude diagrams and star
formation histories in order to directly compare to available observations. The
simulated galaxies formed most of their stars in many $\sim$10 Myr long bursts.
The CDM galaxy has a global SFH, HI 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 spectra.
