Telegram can’t be trusted to not broadcast your pseudonym to whatever work or other contacts you might have saved on your phone.
Telegram doesn’t allow for changing one’s name per group chat like Discord does, so if you want to be known by a certain name only in a certain place, you need another account, which means you need another phone number. That’s not privacy.
As far as message contents go, people can click two buttons to export the entire chat. Or even delete the entire history. Then they’ll have the history and you won’t, and malicious actors (which are everywhere on Telegram) will be able to take your words out of context and use them against you. That’s not privacy.
On Discord at least you have some protections against that by having hoops to jump through to export messages (risking account ban or account creation limitation), helping keep people honest. The account age is also visible in plain sight, and that is very much a data point that people use to ward off potential bad actors.
Another dimension of privacy is I might want to read a message without knowing the sender read it. You may or may not care about that.
If you want to sell drugs and remain private, Telegram might be less likely to report you to the government.
Privacy is not about what features your app might have, it’s about what the user ultimately experiences, and the specific risks they take. The threat model suited for the average person is much more unfavorable on Telegram than on Discord.
It’s more complicated of a situation than being able to say “we can do end to end encryption”.