I would probably correct the question - should you use A.I.R. or Managed File Replication without A.I.R., because normally you wouldn't want to use "Data Domain Replication" which moves data at the directory or MTree level and the only use case for it I can think of is the pool replication if your DD is configured as a VTL in NBU.
Now if asked this way, the question boils down to what is important, for you:
A.I.R. requires a second NBU domain in DR which is extra resources, management overhead, etc, however it does provide a quick way to restore data because it is already in the catalog of the DR master. This has its pros and cons.
Pros: DR restores can be done independently from Production, both masters can be active at the same time.
Cons: A.I.R. replicates only data, not policies. This means you don't have protection for the entire catalog - just for images that were subject to A.I.R. prior to a DR event and you can't run backups from DR without reconfiguration. Another thing to rememeber, you can't A.I.R. images that have been written to Data Domain prior to A.I.R. configuration, there is no way to make the remote NBU master aware of the old images through A.I.R. (there are some methods but they have various degree of associated pain with them).
The standard duplication approach using SLPs will also copy the data using the same method on Data Domain (Managed File Replication) but the operation requires only one Master. If you have a proper HA/DR in place it will protect the domain including the catalog.