We study water transport in bi-disperse porous structures inspired by xylem tissue in vascular plants (arrays of microchannels interconnected by a nanoporous layer). With various experiments (high pressure-driven flow, spontaneous imbibition, transpiration-driven flow at negative pressure), we show that transport rates can be tuned by varying the shape of the microchannels. Even with a fixed shape, spontaneous imbibition behaves very differently depending on sample preparation (air-filled vs. evacuated), because of a dramatic change of transport mechanism in the microchannels. We provide analytical (effective medium) approaches and numerical simulations to rationalize these observations.