In IBM MQ,

If an application sends a persistent message to a non persistent (default) queue, which takes precedent in the event of a failure?

You could simply check this.

1. Create non-persistent queue TEST.
2. Use MQ Explorer for put a message in the queue TEST.
3. Use RFHutil for put a persistent message in the queue TEST.
4. Restart MQ.

The persistent message still in the queue TEST:

display queue(TEST)

QUEUE(TEST) ... CURDEPTH(1) ... DEFPSIST(NO)

The application is responsible for the persistence of messages, so in the event of a failure, the message will not be lost