As a user
Everyone is on an equal playing field
IOW no more comments about how someone’s MUA is messing up threading.
Since everyone uses the same tool there isn’t a need to teach people who do not have an email-heavy life/workflow how to use email effectively and make it work with any of the major browser-based email clients that so many people use these days.
Multi-reply responses
Being able to reply to everyone who has commented since you last read a thread in a single response I find can really help when trying to get across a narrative. (And for those of you who don’t know, you can highlight text in any reply in a topic and have it end up in your current reply, and you can do that multiple times in a single reply.)
You can edit things
The fact that you can go back and edit your posts is really nice, especially if you accidentally were a tad rude and you want to tone something down. It even lets admins fix spelling mistakes. 
Rich formatting via Markdown
Now I know you can use HTML emails, but I have seen enough people complain when they get such emails that I’m calling this out as a separate thing. I mean I can’t even imagine doing an email as nicely formatted as this post is.
This also includes fixing titles so it’s easier to know what a topic is truly about.
As an admin
I can split topics into multiple topics
When a topic veers off-course or splits into a new topic, good luck trying to get people to do a split and actually follow it. With Discourse an admin and forcibly split a conversation into a new topic and that helps keep things on-topic in a discussion. (See this topic as an example
.)
People can flag bad actors in the tool
It is so much easier to get people to flag misbehaving folks here than it is on a mailing list. Convincing people to email admins or the Conduct WG is really hard. Compare that to here will there’s a flag icon sitting right there on every post that people can use which is a much lower barrier to doing the right thing and bringing bad actors to the attention of the admins.
Managing bad actors is so much easier
And I mean so much easier (just imagine I have a ton of emphasis on how so much better this is to get the scale appropriately
). For instance, accounts are in a single place so if we have an issue we can take care of the person and have it ripple through the whole instance; compare that to the mailing lists on mail.python.org where each individual list has to maintain their own suspensions and blocks and so bad actors can continue to operate in other places.
We get notified when someone has been ignored by five or more people as an early warning that someone might be stirring up trouble. That’s really handy compared to people maintaining private kill lists in email where that information never reaches the admins.
Suspensions can be timed. When we hand out e.g. 3 month suspension on a mailing list I have to personally remember to turn off the suspension or have the suspended person reach out to me personally to undo it. Here on Discourse it’s built into the tool, so the suspension undoes itself automatically.
Spam is automatically managed. On mailing lists the solution is to set all new subscribers to moderated to make sure that their initial email is legit and then clear the moderation flag. Here not only is it harder to sign up for an account to do the spamming, but the system detects when someone posts the same link too often.
IOW I’m totally willing to be an admin on this Discourse instance while I constantly contemplate giving up being an admin for mailing lists as it’s just so much more of a hassle.