The dynamic nature of adhesive interface failure remains poorly understood, especially when the contact between the two surfaces is localized in microscopic points of adhesion. Here, we explore the dynamic failure of adhesive interfaces composed of a large number of micron-sized pillars against glass. Surprisingly, we find a large influence of the microcontact geometry; ordered arrays of these pillars exhibit significantly stronger adhesive properties than equivalent surfaces in which the pillars are disordered. This can be understood with a simple geometric argument that accounts for the number of adhesive bonds that needs to be broken simultaneously to propagate the crack front. Moreover, the adhesive strength in both cases depends largely on the velocity with which the surfaces are separated. This rate dependence is explained on the basis of a semi-phenomenological model that describes macroscopic failure as a consequence of microscopic bond-rupture events. Our results suggest that the dynamics of adhesive failure, in the limit explored here, is predominantly stress-driven and highly sensitive to local geometry effects.