Measurements across single grain boundaries in YBCO thin films and bulk bicrystals have been used to demonstrate the influence of grain boundary structure on the critical current carried across the grain boundary. In particular, we show that one role of grain boundary structure is to change the degree of pinning along the boundary, thereby influencing the critical current. This effect can be used to explain the large difference in critical current density across grain boundaries in thin films compared to that for bulk bicrystal. These differences illustrate the distinction between the intrinsic mechanism of coupling across the grain boundary that determines the maximum possible critical current across a boundary and the measured critical current which is limited by dissipation due to the motion of vortices.