One of the biggest advantages have to use Azure AD is the ability to deliver a SSO platform for the entire enterprise.
In our case we implement Azure AD in order to replicate our server AD on-premise in the cloud and offer authenticated access service to our users outside the office and remote branches.
Once implemented in Azure AD we get all of our users agree to the platform and could use both Office 365 business PCs as well as on their mobile devices.
On the other hand, with Azure AD we keep our users connected all the time from online applications Office 365 as well as his own, always using a single authentication method.
Regarding the disadvantages almost you can not name many, unless a VM in Azure has an additional cost this is quickly solved by having replicated AD infrastructure everywhere.
Perhaps one of the things that can be a disadvantage is the speed with which you access the VM in Azure, but resolves having a good internet connection.
Of course I recommend the use of Azure AD for those users who need a centralized platform in Windows environments and especially for those using Office 365. It is a robust, secure and easy platform to deploy and maintain.
As I mentioned before, we can solve the problems in our company was maintaining a consistent and secure SSO structure. With our server replicated in Azure AD we get all the benefits of a heterogeneous environment and safe for the whole organization.