  Cosmic rays (CRs) have recently re-emerged as attractive candidates for
mediating feedback in galaxies because of their long cooling timescales. They
can have energy densities comparable to the thermal gas, but do not suffer
catastrophic cooling losses. Recent simulations have shown that the momentum
and energy deposited by CRs moving with respect to the ambient medium can drive
galactic winds. However, simulations are hampered by our ignorance of the
details of CR transport. Two key limits previously considered model CR
transport as a purely diffusive process (with a constant diffusion coefficient)
and as an advective streaming process. With a series of GADGET simulations, we
compare and contrast the results of these different assumptions. In idealised
three-dimensional galaxy formation models, we show that these two cases result
in significant differences for the galactic wind mass loss rates and star
formation suppression in dwarf galaxies with halo masses
$M\approx10^{10}\,\textrm{M}_\odot$: diffusive CR transport results in more
than ten times larger mass loss rates compared to CR streaming models. We
demonstrate that this is largely due to the excitation of Alfv\'en waves during
the CR streaming process that drains energy from the CR population to the
thermal gas, which is subsequently radiated away. By contrast, CR diffusion
conserves the CR energy in the absence of adiabatic changes and if CRs are
efficiently scattered by Alfv\'en waves that are propagating up the CR
gradient. Moreover, because pressure gradients are preserved by CR streaming,
but not diffusion, the two can have a significantly different dynamical
evolution regardless of this energy exchange. In particular, the constant
diffusion coefficients usually assumed can lead to unphysically high CR fluxes.
