There are protocol properties, and client properties. I think some of both are important.
### Protocol
* Easily federated
* Identifiers can be memorable/meaningful (unlike phone numbers) while still being globally unique (thanks to federation)
* Device independent (not tied to a phone number, can generally use the same account on different devices)
* Can contact people you don't know/haven't met (this is possible with Signal, but they'd have to publicly share their personal cell phone number, which is a no-go).
### Client
* Optimized for longer-form, less immediate messaging (folders, drafts, rich text)
* MIME attachments (Signal supports only a limited number of predefined types of attachments)
I feel like you could probably layer an email-equivalent on top of Matrix, but I'm not 100% sure about that.
### Protocol
* Easily federated
* Identifiers can be memorable/meaningful (unlike phone numbers) while still being globally unique (thanks to federation)
* Device independent (not tied to a phone number, can generally use the same account on different devices)
* Can contact people you don't know/haven't met (this is possible with Signal, but they'd have to publicly share their personal cell phone number, which is a no-go).
### Client
* Optimized for longer-form, less immediate messaging (folders, drafts, rich text)
* MIME attachments (Signal supports only a limited number of predefined types of attachments)
I feel like you could probably layer an email-equivalent on top of Matrix, but I'm not 100% sure about that.