If you need a cloud-based service bus or a simple to use queue/topic/routing/pub-sub service, then Azure Service Bus is a very good choice at a reasonable price and performance. Typically on-premise we'd use RabbitMQ because it "just works", but if you're building a "cloud-first" application, then this is the one to go with. It's especially easy to integrate with if you're already embedded in the Microsoft ecosystem.
If you’re bringing anything into Salesforce you should just invest now into Mule, you will get your money’s worth and find a myriad of uses to build APIs between many other systems. Once you build a component you can easily reuse it as a building block to attach to another source/destination. This makes it easy to ramp up quickly and spread usage of Mule throughout your enterprise. A good value for medium to large companies, but probably cheaper to outsource your job to a consulting firm if you are smaller.
Acting as a basic queuing service it works very well.
One of the best parts is that Azure Service Bus can work over HTTPS which helps in strict firewall situations. There is a performance hit if you choose to use HTTPS.
The routing capabilities are quite good when using topics and subscriptions. You can apply filters using a pseudo-SQL-like language though the correlation filters are quick and easy options.
Costs are very reasonable at low-ish volumes. If you're processing 10's of millions of messages a month... it may be a different story.
It is best suited for Rest API development. Mule ESB uses RAML as an API descriptor which is less complex and easy to understand. RAML is an open standard majorly supported by Mulesoft. Once RAML is developed, it is very easy (a few clicks)to create flows corresponding to the resources defined in the RAML. One can also include JSON schema validation in RAML, and with the use of APIkit router, Mule ESB makes the request validation very easy (it's automatic basically.)
Mule ESB comes with a large spectrum of community and enterprise connectors. We have connectors for all the major platforms like Facebook, Twitter, Salesforce, SAP, etc. This enables Mule ESB to integrate with the other systems in a faster and more robust way. Mule ESB has many components to fulfill the requirements of each integration (for example batch processing, parallel processing, choice, etc.)
Mule API gateway is one of the best tools (modules) of Mulesoft's offering. It supports API governance and management very well. One can easily enforce policies on their APIs with API gateway. It enables some of the must-have features in an API solution (i.e. throttling, oAuth, access levels, etc.)
Implementing a CI/CD (DevOps) environment for Mule ESB is a very easy task. Mule majorly uses MAVEN as its build tool, which in turn makes it best suitable for CI/CD approach. Mule also provides MAVEN plugins for auto deployments to the servers. Mule also has a best Unit testing module which is MUnit. MUnit can be used for both Unit and Functional testing, and it is easy to write and generates coverage reports in various formats.
RabbitMQ is simple and awesome... but so is Azure Service Bus. Both accomplish the same thing but in different environments. If you're building a cloud-native application - especially one that is serverless by design - Azure Service Bus is the only real choice in Azure. It works well, it's performance, and it's reasonably priced in the Standard tier. From our testing, RMQ is more performant, but it's hard to compare service-based implementations vs RMQ installed on VMs.