Organized deep convection plays a critical role in the global water cycle and drives extreme precipitation events in tropical and mid-latitude regions. However, simulating deep convection remains challenging for modern weather forecasts and climate models due to the complex interactions of processes from microscales to mesoscales. Recent models with kilometer-scale (km-scale) horizontal grid spacings (Δx) offer notable improvements in simulating deep convection compared to coarser-resolution models. Still, deficiencies in representing key physical processes, such as entrainment, lead to systematic biases. Additionally, evaluating model outputs using process-oriented observational data remains difficult. In this study, we present an ensemble of MCS simulations with Δx spanning the deep convective grey zone (Δx from 12 km to 125 m) in the Southern Great Plains of the U.S. and the Amazon Basin. Comparing these simulations with Atmospheric Radiation Measurement (ARM) wind profiler observations, we find greater Δx sensitivity in the Amazon Basin compared to the Great Plains. Convective drafts converge structurally at sub-kilometer scales, but some discrepancies, such as too-deep up- and downdrafts and too-weak peak downdrafts in both regions or too-strong updrafts in Amazonian storms remain. Overall, we observe higher Δx sensitivity in the tropics, including an artificial buildup in vertical velocities at five times the Δx, suggesting a need for Δx≤250 m. Nevertheless, bulk convergence - agreement of storm average statistics - is achievable with km-scale simulations within a ±10 % error margin, with Δx=1 km providing a good balance between accuracy and computational cost.