When comparing Taiga vs Discourse, the Slant community recommends Discourse for most people. In the question“What are the best self-hosted reactive OR (in the absence of a reactive option) best-in-class open source web apps aimed at SME?” Discourse is ranked 1st while Taiga is ranked 2nd. The most important reason people chose Discourse is:
Discourse has a simple user trust system that makes moderating the forum a lot easier. Users gain more permissions as they gain more trust, which limits the amount of damage spammers and trolls can do. Discourse co-founder Jeff Atwood also founded StackExchange, which is the gold standard for gamification/moderation systems so you can also expect Discourse to get better and better at moderation.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Supports both Kanban and Scrum modes
User stories can be organized in both Kanban and Scrum task management systems.
Pro Free and open source
Taiga is licensed under GPL with source code available on GitHub.
Pro Simple to use
Pro Comprehensive Agile software development toolset
Taiga tries offering a complete Agile software development toolset. It includes complete solutions for issue tracking, videoconferencing, documentation (in the form of a wiki) and either a backlog or a Kanban board for managing user stories.
Pro Built-in issue tracking
Taiga has built-in issue tracking tools. The issues can be organized by user-defined type, severity, priority, creation date, assignee, creator, tags as well as filtered by subject. Taiga can also integrate with GitHub, GitLab and BitBucket.
Pro Built-in wiki
Each project has a wiki. It has Markdown support as well as a WYSIWYG editor.
Pro Built-in video conferencing tools
Integrates with either AppearIn or Talky to provide a video conferencing solution.
Pro Migration from RedMine
Pro Export/Import feature
You can extract all your data from one Taiga instance and move it to another one. You can read more here.

Pro Has a built-in immune system from trolls, spammers and bad actors
Discourse has a simple user trust system that makes moderating the forum a lot easier. Users gain more permissions as they gain more trust, which limits the amount of damage spammers and trolls can do. Discourse co-founder Jeff Atwood also founded StackExchange, which is the gold standard for gamification/moderation systems so you can also expect Discourse to get better and better at moderation.

Pro 100% free and fully open source
Discourse is powered by Ruby on Rails, Ember.js, PostgreSQL and Redis. The code is licensed under GPL and available on GitHub.
Pro Modern & polished UI/UX with lots of great smaller features
The best feature is its design: discourse is designed to aid in the creation of high quality online conversations. Flat discussions with well implemented quoting systems, expandable/collapsible replies, infinite scroll, clean UI and many more features come together to form a highly polished forum experience that makes legacy forums show their age.
Pro Helpful community
Discourse has a comprehensive forum culture support hub at meta.discourse.org.
Pro Hosted and self-hosted solutions
You can host it yourself in a $5 cloud server or on any Linux server you already have. And if you don't want to deal with this, you can use the hosting platform from the development team.

Pro Live preview while editing the post
The post editor has a synchronized side-by-side preview of the Markdown rendering of the post.
Pro User selectable themes
Users can choose between the themes made avaliable on their instances, and even use different themes on different devices (mobile vs desktop, for example).

Pro Export your posts

Pro Effective search
Pro Good to go out of the box yet infinitely tweakable
Discourse has sane, safe out of the box defaults, but a million dials and knobs to tweak.

Pro Easy one-click upgrade
Discourse can upgrade itself with one click in the admin panel. Not the same can be said about MyBB, or most other forums.
Pro Advanced JavaScript app
Runs in modern browsers and works identically on desktop and tablet and smartphone without the need for a native app.

Pro Discussions can be organized in categories and tagged
Discussions can be tagged with an arbitrary number of tags, separately from categories. Categories are hierarchical and don't scale; tags do.

Pro Official Akismet Anti-Spam Plugin
Official Akismet plugin vets posts by new users to make sure they don’t look spammy before they hit your site. Akismet key purchase required.

Pro Extensible via plugins
Pro Good on-boarding experience for new users
New users are greeted withe the disco bot which has an interactive experience to teach the basics of using Discourse.
Cons
Con No Kanban metrics
Taiga is said to support Kanban but it does not generate any of the usual Kanban metrics (cycle time, lead time) or graph (Cumulated Flow Diagram).
Con Can be overwhelming at first
Taiga presents users with a lot of information and functionality right from the beginning with little guidance. Figuring how stuff works might take a bit.
Con Too much functionality for small projects
While it's possible to disable any unwanted features (modules), the amount of functionality that's present might be more than a small, short-term project needs.

Con Complicated setup
Compared to standard PHP+MySQL apps, Discourse is more complicated - the app lives in a Docker container. However, a Docker image is available, which reduces the setup time to about 30 minutes.
Con Leaves out users with shared hosting
Discourse requires sudo, which is only available on a VPS.
Con Bad noscript support
When using a Discourse forum without scripts the experience is greatly reduced. It's really hard to use and is read-only, meaning that one can't comment or create threads without scripts.
Con It is more "Free to Try" than really free
Discourse is open source free software. The hosting is where the costs come in. Discourse.org hosting starts at $100/mo, but you can pay as little as $5/mo on Digital Ocean or other cloud hosts.
Con Extremely expensive hosting
Official discourse.org hosting starts at $100/mo and supports the team creating the software. It can also be hosted on a cloud service like Digital Ocean for $5/mo.
