Azure is less friendly as a technology practitioner (compared to working with AWS), but I fully appreciate the value you describe. Does AWS have Active Directory as a first class citizen? Office 365? Outlook/Exchange? No.
AWS does offer AD as a first class citizen... More than Azure.
AzureAD is not Active Directory, and unless something has changed a lot in the last year (maybe it has?), Azure does not offer anything that looks, smells, and feels like on-prem AD in the cloud.
Azure Active Directory Domain Services is full-fat AD, but they market it towards only using it for services in Azure. But you can set up a VPN from Azure to join on-prem stuff (or to replicate existing AD to Azure).
That's good to hear! I really wanted "hosted AD" from a cloud a few years ago, and Azure definitely did not offer this... or they marketed it so poorly I could not find it anywhere. :(
AWS has straight up guides for do's/dont's, and various ways to integrate their AD service with yours, including multiple scenarios such as running them as the masters of the forest, with read-only's on-site, and vice-versa.