When comparing TeamWork.com vs Emacs Org-mode, the Slant community recommends Emacs Org-mode for most people. In the question“What are the best cross-platform task apps?” Emacs Org-mode is ranked 2nd while TeamWork.com is ranked 51st. The most important reason people chose Emacs Org-mode is:
This app's flexibility is based on its minimalist approach, giving the user near-infinite freedom.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Offers lots of granularity in task management
Tasks are grouped in task lists and can have subtasks. Each task list can be assigned to a particular set of users, aligned with a milestone and have notes. Each task in the task list can have a description, a start and a due date, attachments, priority, manually set progress, followers, dependencies, be assigned to a particular set of users and set to repeat. Each subtask has the same configurable properties except instead of the ability to assign people, subtasks can be commented on.
Pro Each project has only the required functionality
It's possible to limit projects only to the necessary features so that unnecessary functionality doesn't get in the way and clutter up the interface.
Pro Good assortment of features
Gantt charts, calendar and an easy overview of huge amount tasks.

Pro Ultimate flexibility
This app's flexibility is based on its minimalist approach, giving the user near-infinite freedom.
Pro Absolutely free
Emacs with Org-mode is free as in beer and free as in speech – that is, it costs nothing and it’s totally open source.

Pro Files are usable anywhere at anytime
Users are not tied to one service provider, program, platform, or database engine.

Pro Incredibly extensible
There are many plug-ins for Org-mode, including Org-habits and Org-notify. If Org-mode lacks some piece of functionality, it is very easy to add it.
Pro Agenda views
Pro Excellent unofficial Android app (orgzly)

Pro Offline support
Pro Efficient features for deadline organization
Pro Supports plaintext spreadsheets
Pro There are a lot of extensions, for exporting to html, bootstrap, js-reveal and much more
Pro Quickly add rich text
Cons
Con Provides too much detail for small projects
Amount of granularity for tasks can be overwhelming for small projects or teams.
Con Unintuitive user interface
The key combinations are unintuitive and difficult to remember. This is probably because there are a lot of hidden "modes" depending on where the cursor is. Actions aren't paired with reversing actions like in other todo apps. For example, hitting shift-tab does NOT reverse the effect of hitting tab.


Con Android app isn't very good
There are several user-created apps for Android, but none seem to offer the same level of functionality as other to-do apps.
Con Not really cross platform
Although it is possible to get a lot of it working, no all in one, sync included, out of the box solution is available for mobile devices.
Con By default, a hard-to-read display
The default way of writing an outline or checklist creates a very messy wall of text that's difficult to read with no vertical spacing. You can manually add vertical spacing, but the Org operations don't preserve it. There are pretty-display modes, but you need to remember how to enable them, etc. etc.
