What is the biggest difference between EMC Data Domain and Rubrik?

As Neil Mistry said, they are quite different products: Rubrik is a complete solution where Data Domain is deduplicating storage that requires software to drive. I used to manage a B&R for a company that had a Data Domain in each data center which supported 4, Tivoli Storage Manager instances at each site and the Data Domain replicated all data cross-site. It was a simple setup but we did run into some performance issues since our TSM servers were all VMs and networking inside VMware is hard to determine performance. In the end, the customer didn't like the cost of DD disk and our devices ran out of capacity. Turns out only database full backups deduplicate well. All else, including transaction logs, can go to much less expensive disk and simply be compressed.

The biggest difference is Rubrik has native software and hardware on one platform. Data Domain is only a disk target and a very good one but you still need backup software such as Networker, Veritas, Commvault, etc. That software requires both a master and media server which drives a lot of complexity. Rubrik is hyperconverged data management, there is not software licensing, end of year true-ups or additional infrastructure. Policy-based backup and restore functions with cloud archiving integration. It’s also really fast! Finally, if you’re running Nutanix and its native hypervisor AHV then Rubrik can protect that hypervisor and VMware.

I agree with the other answers - With Data Domain, you still require a software solution to go with the back-end storage. I.e., Avamar, Networker, etc.
Rubrik is a Software Defined Solution or can be deployed with its own set of hardware\storage.