Kafka and ActiveMQ may have some overlaps but they were originally designed for different purposes. So comparing them is just like comparing an Apple and an Orange.
Kafka
Kafka is a distributed streaming platform with very good horizontal scaling capability. It allows applications to process and re-process streamed data on disk. Due to it’s high throughput it’s commonly used for real-time data streaming.
ActiveMQ
ActiveMQ is a general-purpose message broker that supports several messaging protocols such as AMQP, STOMP, MQTT. It supports more complicated message routing patterns as well as the Enterprise Integration Patterns. In general it is mainly used for integration between applications/services especially in a Service Oriented Architecture.