Pervasive cirrus clouds in the upper troposphere and tropical tropopause layer (TTL) influence the climate by altering the top-of-atmosphere radiation balance and stratospheric water vapor budget. These cirrus are often associated with deep convection, which global climate models must parameterize and struggle to accurately simulate. By comparing high-resolution global storm-resolving models from the Dynamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains (DYAMOND) intercomparison that explicitly simulate deep convection to satellite observations, we assess how well these models simulate deep convection, convectively generated cirrus, and deep convective injection of water into the TTL over representative tropical land and ocean regions. The DYAMOND models simulate deep convective precipitation, organization, and cloud structure fairly well over land and ocean regions, but with clear intermodel differences. All models produce frequent overshooting convection whose strongest updrafts humidify the TTL and are its main source of frozen water. Inter-model differences in cloud properties and convective injection exceed differences between land and ocean regions in each model. We argue that global storm-resolving models can better represent tropical cirrus and deep convection in present and future climates than coarser-resolution climate models. To realize this potential, they must use available observations to perfect their ice microphysics and dynamical flow solvers.