Hi Matthew and John,
> ... deploying the ArcGIS Enterprise stack in Azure or AWS. Does anyone have any experience doing this? Willing to share any pros/cons both from a technical and/or business perspective? Hybrid vs full cloud deployments?
Please take a look at this whitepaper, https://community.esri.com/groups/mobile-gis/blog/2017/10/25/arcgis-secure-mobile-implementation-pat... specifically section 5 - which discusses the different deployment options available for the ArcGIS Platform. It discusses pros/cons from a technical and business perspective(s).
FYI: I am in the process of updating this whitepaper to include content on the ArcGIS user types, GIS server roles, etc. The updated version should be available end of Oct/mid Nov 2019 timeframe.
Hope this helps,