As anyone who's followed a giant email chain, I think that slack is at-least a little bit easier to follow. Albeit I'm working in a company that is just now trying to start to emphasize stories/tickets/chat over email for everything, with tons of pushback.
Gone are the days of email everything, tons of people are CC'd, email chains are 30-50 responses in. It's absolutely unmanageable. Oh and if you drop chat, let's start logging alerts to email, or bugs to email. It's useless.
Personally I'll use chat for anything relatively quick or unimportant in the grand scheme of things. I'll use email for when it's not something that requires a response right away but generally is also unimportant to the company projects and doesn't involve a ton of collaboration. Anything bigger than that goes in a system that's suitable for tracking projects or complicated topics.
I don't think there's a one size fits all solution for communication.
I've convinced everyone at two companies so far (50 and 20 people) to never reply directly in a channel, and always use threads:
I usually start by proposing an idea to a small group of people - e.g. my team or people at the company I think might like the idea. Only after a few people say they like the idea and start using threads, propose the idea to more people and say "look, a few of us are using threads and it works".
Or never start to use it in the first place.
The fundamental problem with Slack is that its interactions are not structure in the right way to be useful in non-real-time. An email thread has two critical pieces of structure that Slack threads lack: a subject line, and a beginning. With email, it's easy to tell where a particular discussion started, and which messages have to do with that discussion. On Slack, these things are all intertwingled. In order to find the beginning of a discussion you have to scan everything in the channel. That is what makes Slack a distraction. It's much harder (like virtually impossible) to filter content by topic after the fact.