While you can schedule message delivery in ActiveMQ it wasn't designed to be used as a job scheduler whereas that's exactly what Quartz was designed for.
In one of your comments you talked about wanting a "scalable solution" and ActiveMQ won't scale well with a huge number of scheduled jobs because the more messages which accumulate in the queues the worse it will perform since it will ultimately have to page those messages to disk rather than keeping them in memory. ActiveMQ, like most message brokers, was meant to hold messages for a relatively short amount of time before they are consumed. It's much different than a database which is better suited for this use-case. Quartz should scale better than ActiveMQ for a large number of jobs for this reason.
Also, the complexity of the jobs you can configure in Quartz is greater. If you go with ActiveMQ and you eventually need more functionality than it supports then that complexity will be pushed down into your application code. However, there's a fair chance could simply do what you want with Quartz since it was designed as a job scheduler.
Lastly, a database is more straight-forward to maintain than a message broker in my opinion and a database is also easy to provision in most cloud providers. I'd recommend you go with Quartz.