Both would do the trick, but there are some nuances. We work with both.
From the sound of it, your main focus is "not losing messages". In that case, I would go with RabbitMQ with a high availability policy (ha-mode=all) and a main/retry/error queue pattern.
Push messages to an exchange, which sends them to the main queue.
If an error occurs, push the errored out message to the retry exchange, which forwards it to the retry queue. Give the retry queue a x-message-ttl and set the main exchange as a dead-letter-exchange.
If your message has been retried several times, push it to the error exchange, where the message can remain until someone has time to look at it.
This is a very useful and resilient pattern that allows you to never lose messages. With the high availability policy, you make sure that if one of your rabbitmq nodes dies, another can take over and messages are already mirrored to it.
This is not really possible with SQS, because SQS is a lot more focused on throughput and scaling. Combined with SNS it can do interesting things like deduplication of messages and such. That said, one thing core to its design is that messages have a maximum retention time. The idea is that a message that has stayed in an SQS queue for a while serves no more purpose after a while, so it gets removed - so as to not block up any listener resources for a long time. You can also set up a DLQ here, but these similarly do not hold onto messages forever. Since you seem to depend on messages surviving at all cost, I would suggest that the scaling/throughput benefit of SQS does not outweigh the difference in approach to messages there.