Okay, the chat itself in Steam is pretty fast (unless you attempt to send an emote). The problem is, there's zero message delivery guarantees, and the client doesn't even care to inform you whether the message has been successfully sent. If you're on an unreliable internet connection, your best bet is to close and re-open the chat window to see whether the messages made it to the server in the mini chat log that shows the last 2-5 messages (that's the extent of the client's chat history feature by the way). It's an usability nightmare.
This isn't about how fast Discord is but about how bad of a job Valve is doing (I'm not even certain present tense applies here given that the chat client has essentially not received any major new features for like a decade).