There's no (that I know of) to export channel logs from Discord, nor to log to an external text file.
That means that if I'm interested in something that was discussed at some point in the past, I have to either use Discord's crappy search feature, or manually scroll back and manually scan through text to try to find what I'm interested in.
Discord's scrollback is slow and painful.
By contrast, IRC logs are just plain text files, so I can use powerful regexes or a plethora of text search/manipulation tools to work with them, and scrolling back through text logs is super fast... especially in a decent editor like vim or emacs.
I also own my own logs, and don't need to be connected to any server to read them. Reading/searching through logs can be done completely offline.
If Discord decides to ban you or some channel/server you're interested in goes down (permanently or even temporarily), you're completely screwed. You'll never get the information you're interested in out of it.
The only substantial advantage of Discord I can see over IRC is inline images (which are often just an annoyance, but can sometimes be useful) and voice chat.
Other than that it's bloated, opaque, and a worse experience for me than IRC.