I think part of the sell is how we would manage the admin component of a Message Queue, which tilts things towards Azure Message Queues as it's PaaS. We're mostly IaaS at the moment, and starting to see some of the admin overhead that comes with managing that infrastructure ourselves. We're not ready to jump onto a PaaS solution for the things we've grown accustomed to managing, but for something brand new, I think my company would be open to it.
Architecturally, we'd lean on it initially for background job processing, which is currently at a scale where our homegrown, db-backed solution is starting to show it's weaknesses. Once it's in place though, I think it could leveraged as a key component to decouple subsections our application and give us more flexibility with scaling and deployment.