S/MIME and Azure AIP aren't really interchangeable and one doesn't replace another. AIP provide persistent data privacy (on a storage), while S/MIME provide data privacy on transport.
The following features provided by S/MIME and not provided by AIP
- S/MIME is a public standard (latest RFC revision is RFC 8551). This means that 3rd party interoperable tools can be used to handle S/MIME. AIP is not.
- S/MIME operates only on email transport and provide end-to-end content privacy, including email body and attachments. AIP does not.
- S/MIME is often integrated in email client and does not require any dependencies on tools or Azure. AIP does require dependencies and infrastructure.
I would say that S/MIME and AIP complement each other, but whether to use both -- depends on your security and threat model.