The performance of ELMy H-mode operation in ASDEX Upgrade and JET is compared. Special attention is paid to variations (usually reductions) in this performance near the operational limits which will need to be approached in a next step device. In JET it is found that input powers substantially above the H-mode threshold power are required to obtain discharges with energy confinement enhancement factors at or above the usual ELMy H-mode scalings. Such a margin (as much as a factor of two in JET) is not observed in ASDEX Upgrade. It is proposed that this difference may be due to the higher edge collisionality in ASDEX and the results are compared to a recent theory based on interchange instabilities and magnetic flutter. In ASDEX Upgrade, the confinement in Type I ELMy discharges degrades as the density is raised due to a stiffness of the temperature profiles which leads to a degradation of the core confinement. This type of stiffness is observed in JET only at relatively high edge densities. In JET, the edge confinement degrades as the density is increased by external gas fuelling, consistent with a constant edge pressure gradient and an edge barrier width which reduces in proportion to the edge ion poloidal Larmor radius. In both machines, H-mode performance is limited at high density by a transition first to the Type III ELM regime and then to L-mode. The confinement penalty, relative to good Type I ELM discharges, of operating with Type III ELMs is about 25-30%. The maximum densities for operation with Type I or Type III ELMs can be substantially increased by increasing the plasma triangularity in both machines.