Information on App Services or Kubernetes on Azure
Azure App Service:
Azure App Service enables you to build and host web apps, mobile back ends, and RESTful APIs in the programming language of your choice without managing infrastructure. It offers auto-scaling and high availability, supports both Windows and Linux, and enables automated deployments from GitHub, Azure DevOps, or any Git repo.
Azure Functions: If an application needs an HTTP endpoint for a potentially long running process without getting into a elaborate programming model, Azure Functions is a good option. They can be developed as an extension of an existing application. They support routing based endpoints similar to an API. They support AAD and other authentication, SSL, Custom Domain, RBAC, etc. They have a good CI/CD support as well. They are in the process of integrating .Net Core support. So if you are looking to get a simple application model and don't want to get into setting up/managing underlying infrastructure, Azure Functions is good choice.
Azure Kubernetes Service (AKS): As application development moves towards a container-based approach, the need to orchestrate and manage resources is important. Kubernetes is the leading platform that provides the ability to provide reliable scheduling of fault-tolerant application workloads. Azure Kubernetes Service (AKS) is a managed Kubernetes offering that further simplifies container-based application deployment and management. AKS manages your hosted Kubernetes environment, making it quick and easy to deploy and manage containerized applications without container orchestration expertise. It also eliminates the burden of ongoing operations and maintenance by provisioning, upgrading, and scaling resources on demand, without taking your applications offline.
How do you choose?
Azure Kubernetes Service (AKS) manages your hosted Kubernetes environment, making it quick and easy to deploy and manage containerized applications without container orchestration expertise. So that means you need to pay for VMs. Only pay for the virtual machines instances, storage and networking resources consumed by your Kubernetes cluster.
App service for container will deploy the containerized app with your preferred dependencies to production in seconds. You need to pay only for App plan.