Inbox Zero actually takes action on your emails for you using AI, automatically labeling, organizing, and unsubscribing from newsletters without you having to do it manually. That means your inbox gets sorted and cleared out as you go, so you don't have to keep cleaning up the same mess over and over.
Mailman, on the other hand, is focused on controlling when emails hit your inbox. It batches deliveries or requires approval for new senders, so you're less distracted, but it doesn't organize or process the emails themselves. You still have to handle all the clutter and newsletters on your own.
If you want your inbox to be actively managed and made less overwhelming through automation, Inbox Zero is the better pick. Choose Mailman only if your main problem is the timing of email interruptions, not the actual mess inside your inbox.