A new class of convection-permitting global atmosphere models is emerging for Earth system modeling. These state-of-the-art models can directly simulate convective storms and hold promise for improving modeling hydrological extremes and their potential changes in future climates. The DYAMOND project (Stevens et al. 2019) provides an intercomparison framework for these global convection-permitting models with sub-10 km horizontal grid spacing. We recently assessed the fidelity of the convective storms simulated by DYAMOND models against high-resolution satellite observations (Feng et al. 2023) and found a surprisingly large inter-model spread in the simulated frequency of ordinary deep convection and mesoscale convective systems (MCSs). By applying a novel technique to track MCSs, we found that most models captured important MCS characteristics such as the lifetime, rainfall amount, movement speeds, and their diurnal cycle, representing a notable improvement compared to typical global models with coarser resolutions. However, the DYAMOND models significantly overestimated convective rainfall intensity over both land and ocean, while consistently underestimating MCS rainfall area. Recent works also showed that different feature tracking algorithms have significant impacts on assessing MCS characteristics including frequency, size, lifetime and their contribution to total precipitation. To further investigate how feature tracking methods affect the evaluation of global MCS simulations and our understanding of convective organization in observations and high-resolution simulations, we are organizing a new initiative called MCSMIP (MCS tracking Method Intercomparison Project). In this talk, we will present analyses of MCS evaluation in DYAMOND simulations from multiple feature tracking formulations. Potential paths towards more process-oriented model diagnostics to better understand the differences in simulated storm and precipitation characteristics will be discussed.