There are many benefits that an actor model like AKKA.net bring to the table like scalability, reactiveness, in memory-caching etc... When I tried to compare AKKA with Azure Service Bus Queues, I see pretty much the same primary benefits in Azure Service Bus except the benefit of in-memory caching.
In a production environment, AKKA requires multiple VMs with more memory, processing power to handle millions of actors in memory. In the case of Azure Service Bus Queues, powerful hosts are not needed. Even if we use actor model, there is no need of doing supervision or creating the actor system to manage millions of actors. The scalability is automatic with Azure Service Bus.
In a long run, I think Azure Service Bus Queues is cost effective. There is no IT admin required to manage it as the load increases. There is no need of powerful systems too with multiple cores.
Is AKKA actor model suitable for on-premises data centers that have systems with multi-cores and not suitable for apps that can use Azure services when thinking in terms of cost-effectiveness?