I found the forum really useful in the following two ways.
1. I have a well-defined question (which is often open-ended), and forum is a great place to bounce ideas with. However, it’s difficult to ask followup questions more than twice for iterations, so it works very well for well-defined questions, not so well if you expect iterations or have room for redefining your goals.
2. The search function is vey powerful especially when revisiting materials.
Slack is realtime and you can afford to tackle an ambiguous challenge. Reading a paper is not ambiguous, the process of developing an understanding however is an iterative and sometimes ambiguous one. In the case of deep learning, the additional challenge to map the math to the code can add much more uncertainty. In both challenges, it was really nice to work together with @even. Slack has more intuitive UI and more frictionless UX compared the "mailinglist-like" experience of Discourse.
These are my personal opinions based on my very limited usage of private chat on Discourse. I would love to hear how other folks use chat function more successfully and learn to do it myself. I do agree with @jeremy that having everything in one place is so much nicer than splitting it over multiple places. Let me know if I can clarify any additional points.