XMPP is more comparable to Signal, yes.
XMPP allows unencrypted messages and leaks metadata - Signal does neither.
Signal does need (yes, need) a phone number, and most people only have one so that is identifiable info.
Signal is basically a privacy enhanced text/SMS/phone replacement. I can give my phone to someone in person and they can immediately start “texting” me on Signal - this is a feature (as well as a con to some people).
This puts it at mostly the same level as some competitors, including WhatsApp which is often advised against.
People advise against Whatsapp because while it uses Signal to encrypt message contents, they take no effort to minimize the collection of metadata - Signal’s been compelled by court to present all data it has on its users various times and the only info they have is the day/time you signed up for their services and the last day (not time) one of your clients pinged their servers - Source: https://signal.org/bigbrother/
I have yet to find any other free service that collects this little information and works just as well as a normal non-encrypted messenger. Even Signals sticker packs are end-to-end encrypted - Source: https://signal.org/blog/make-privacy-stick/
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