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 …
1) Securing your back-end APIs - If you have a legacy back-end web service that has a basic authentication scheme, you can add some additional security by placing APIM in front, and requiring subscription keys. Leverage your existing firewall to ensure only your APIM instance can communicate with your back-end API, and you've basically added a layer of protection.
2) Lift and shift - there are always going to be clients that don't want to update their clients to use a newer API; in some cases you can make a newer API look like an older one by implementing some complex policies in APIM. You can also do the opposite, making older APIs look new, such as making an XML back-end accept both JSON and XML.
3) Centralizing your APIs - if you've acquired another company and want to make their API set look as if it's a part of the larger whole, APIM is an easy way to provide a consistent front-end interface for developers.
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.
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.
Lack of robustness is a bit of an issue. Several other providers offer more options and capabilities, but then, they are lacking in interface ease.
As with anything Azure, pricing is really hard to stay on top of. I always find that you really don’t know what you’re paying for until you get the bill. Having an excellent Azure Administrator can help resolve that.
Integrating with app services outside of Azure can be a challenge, or at least much more challenging than just using Azure App Services.
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.