Changes in aerosols have been found to counteract the effect of greenhouse gasses (GhGs) on tropical cyclone (TC) activity in the historical record. However, global aerosol emissions have declined in recent decades, a trend projected into the future in most CMIP6 Shared Socioeconomic Pathways (SSP). This study uses experiments from the Energy Exascale Earth System Model (E3SM) to compare the influence on TC activity of: i) the atmospheric effect of aerosols under specified sea-surface temperatures (SSTs); and ii) the net effect of GhGs (including changes in SSTs). The experiments were performed using the CMIP6 SSP5-8.5 emissions scenario with GhG-induced SST warming specified and atmospheric aerosol effects simulated but without explicit ocean coupling. Insignificant changes in global TC frequency were found in response to the atmospheric effect of future aerosols and GhGs, as significant regional responses in TC frequency counteract each other. Future GhGs contribute to more frequent TCs in the North Atlantic, and reductions over the Northwestern Pacific and Southern Indian Ocean. The atmospheric effect of future aerosols drives more frequent TCs over the Northwestern Pacific and reductions over the Northeast Pacific and North Atlantic. Along with increases in TC intensity, global TC precipitation (TCP) is projected to increase by 52.8% (14.1%/K) due to the combined effect of future aerosols and GhGs. Although both forcings contribute to TCP increases (14.7-19.3% from reduced aerosols alone and 28.1-33.3% from increased GhGs alone), they lead to different responses in the spatial structure of TCP. TCP increases preferentially in the inner-core due to increased GhGs, whereas TCP decreases in the inner-core and increases in the outer-bands in response to the atmospheric effects of decreased aerosols. The total TCP increases show signs of both patterns, with a more modest precipitation increase in the inner-core than due to GhGs alone. This research highlights the importance of proper representation of the spatial distribution of aerosols when studying future projections of tropical cyclone frequency and precipitation.