Abstract Cosmic rays (CRs) have recently re-emerged as attractive candidates for mediating feedback in galaxies because of their long cooling time-scales. 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 constant diffusion coefficient) and as an advective streaming process. With a series of gadget simulations, we compare the results of these different assumptions. In idealized 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 ≈ 1010 M⊙: diffusive CR transport results in more than 10 times larger mass-loss rates compared to CR streaming models. We demonstrate that this is largely due to the excitation of Alfvén 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 Alfvén 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.