Metadata. Requiring a phone number to register. And a hostile anti-federation, anti-API stance by Signal. Sure, you can run your own server, but you can't connect to anyone in the official Signal network, and third-party apps are also disallowed.

Wire has the same problem, don't get me wrong. They've been resolutely refusing any third-party connections (mainly requests from Matrix bridge folks). But Signal isn't an improvement on these fonts.

Update 2023-09-28

Edits include addl feature discussion, but mainly an update on Session.

~Nope.~ Maybe?

• Session looks very promising, and I'm trying it right now with my wife. She's much better at catching software warts - if she starts using it more than the N other ways (she currently has Jami, Element, SMS, and now Session on her phone), then I'll know it's a hit. It is lacking a critical feature for phone use: editing previous messages, and it'd be nice if it had Jami's location-sharing. Security and anonymity looks good.
• Matrix is promising, but encryption is still extremely brittle, and prevents me from inviting non-technical F&F.
• SimpleX is promising, but without multi-device support, it's a non-starter.
• Jami is promising, but I can't get the client to work on Arch (it just segfaults), and the answer to my ticket was "Arch isn't supported." In my case, it's because my Qt was newer than their required version - it compiled, but just segfaulted. I lost interest at that point. Notifications are unreliable, as is message delivery. It fails the wife test. It does have a great realtime location sharing feature, which is super handy for, e.g., picking people up at the airport, but that's not enough of a killer feature top overcome the reliability issues.
• Tox - Shoot. I try Tox every once in a while. I know that I uninstalled it once because the mobile app sucked my battery down, but I don't remember if it has some fundamental flaw. I think it doesn't support multi-device? I'll have to check it again.
• Lichat looked interesting, but Ocelot hasn't been updated since '21; it's a small project with not a lot of documentation beyond the spec

~I may have looked at Session at one point, but don't remember why I put it in the No category. I'll have to review it again.~ See my update at top. Session is currently a contender.

XMPP may be the elephant in the room. I used XMPP for years, back before Google supported it, and after. I know a lot of people advocate it, and I think it's a reasonable option; it's certainly well-established. It leaks a lot of metadata, but then, it wasn't designed with security in mind - all of the security has been bolted on after the fact, frankenstein mode. So has multi-participant chat. In fact, most features have been tacked on, and I guess that's why I avoid it these days. Nothing seems well-integrated and reliably functioning. But YMMV; it may be the best option at the moment.

XMPP