ZeroMQ is fast but you need to build build reliability yourself. There are a number of patterns described in the zeromq guide. I have used RabbitMQ before which gives lot of functionality out of the box, you can probably use the worker queues example from the tutorial, it can also persists messages in the queue.
I haven't used Amazon SQS before. Another tool you could use is Kafka.
Amazon seems to offer a number of messaging solutions. The simplest is Amazon SQS, yes. Another is Amazon MQ if you wish to have a hosted RabbitMQ or ActiveMQ messaging platform that is compatible with JMS/AMQP. You will want to measure your needs against the constraints of your messaging scenarios. If you have a small team and you're already on AWS, a quick working solution would be to use the ready-to-go solutions from AWS. My guess is that it would cost more to hire (an) engineer(s) to build/maintain your messaging queue than to use the service-at-scale solutions of AWS. If you have a non-global messaging system you could also consider deploying your own small cluster using RabbitMQ as suggested by Shishir. Another excellent solution might be NATS.io which has a strong community, impressive performance, and is backed by CNCF.
I admit there are a lot of options -- if you wish to own and grow your messaging needs in house, then hire a team and start building. ZMQ is flexible but you will need to write the persistency module and adapt the clustering to your needs. Kafka is a resilient and distributed solution, but it requires an operations team to maintain and handle load-balancing. RabbitMQ seems to be the defacto for getting up and running but can eventually encounter clustering and scaling issues. And on the other hand, the giants offer ready-to-go messaging solutions that end up costing you little, but risk to vendor lock you if you're not careful.
I suppose I ultimately vote for taking the AWS solution -- but check the SLA and performance criteria of your service.