Representing aerosol impacts on liquid clouds is a persistent source of uncertainty in Earth System Models for climate projections due partly to insufficient understanding of complex multi-scale aerosol-cloud interactions (ACI). To address this challenge, we assess the aerosol and ACI features at both traditional 1-degree and 3-km resolutions using the Energy Exascale Earth System Model (E3SM) configured with Regionally Refined Meshes (RRM) to reduce model cost. We focus on four geographical regions to cover a wide range of aerosol and cloud conditions: Central US, Eastern North Atlantic, Northeastern Pacific, and Southern Ocean. Simulation results are evaluated against in-situ and remote sensing observations using a newly developed Earth System Model Aerosol-Cloud Diagnostics package (ESMAC Diags). The coarse-resolution E3SM largely reproduces the kilometer-scale E3SM in terms of aerosol and cloud properties, such as aerosol mixing state and size distribution, cloud droplet size distribution and microphysical processes. However, we find that the N_d-CCN relationship is better characterized in 3-km RRM than 1-degree E3SM, indicating that the highly efficient droplet nucleation bias in the coarse-resolution model can be reduced by increasing model resolution. This study introduces a framework to assess the resolution sensitivity and physical representations in a consistent modeling framework. This framework is useful for model development and evaluation at the convection-permitting scale with a low computational cost.