Selection by use case of SaaS, PaaS, or IaaS
Each model you learned, including the on-premises model, has advantages and disadvantages. The one you should choose depends on your specific business requirements, what features are needed, and the developers and testers that comprise your team. You might need a fully out-of-the-box solution, and time to market might be a more important consideration than price. Or perhaps you have regulatory constraints that force you to have complete control of the environment. AWS offers a lot of assurances regarding their Service Level Agreements (SLAs) and compliance certifications. The more levels in the stack you decide to manage, the more effort you will exert to verify that your systems comply with the different regulations.
In general, one good rule of thumb is to let AWS take over the management of your resources whenever possible. You only take over the responsibility whenever necessary. For example, could you imagine trying to implement the functionality...