The difference between Azure Event Hub, Kafka, and Memphis is in their cost and how to access each one.
Essentially, they are all messaging middleware tools but Azure Event Hub is not free, whereas Kafka and Memphis are free.

Azure Event Hub is a data ingestion service.
As its name suggests, it is from Microsoft Azure.
You can only access it from within Azure and you need an Azure account.
It has pricing.
It is powerful in itself, it has Microsoft’s backing.
But it is not open-source. Azure Event Hub has the option to connect to Kafka without code changes. 

Kafka and Memphis are full-blown message brokers.
They are open-source and are fully free to all.
While Kafka uses a consumer polling system for its architecture, Memphis pushes messages to consumers instead.