- Telegram uses usernames instead of phone numbers by default, which is good if you're using it as an IRC replacement instead of an SMS replacement.
- You can have the client open on essentially unlimited devices simultaneously, including a web app if you need it.
- Messages can be edited at any point after sending with no expiry.
- You can schedule messages to send later, or send a message silently so it doesn't wake people up.
- Different group types - announcement channels, Discord-style groups with sub-channels, flexible moderator roles, etc. (I believe WhatsApp has some of this.)
- Support for bots, which is also very helpful for managing large communities.
- Community-created, sharable stickers. Seriously, people underestimate how nice these are.
The downside is that a lot of this requires state to be stored on the Telegram servers, so most chat's aren't E2E encrypted. (They do have an option for E2E encrypted private 1:1 chats, but you lose most of the polish by using that.)
Also, the official apps are open source, so you can modify them if needed.