When comparing Emacs Org-mode vs Checkvist, 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 3rd while Checkvist is ranked 20th. 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 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
Pro As simple or as complex as you need
Checkvist hits a sweet spot between minimal and complexity. It gives you a host of options and extras to use on your lists, but you can completely ignore them if you don't need them and keep it very simple. This makes Checkvist a one-stop shop, regardless of what type of 'list' you need.
Pro Tasks can be managed with custom tags
Pro vim-like commands
Pro Convenient search by text or tag filtering
Pro Converts incoming emails to todos - this is a way to enter tasks from anywhere.
Pro Great search
Search filters help you search for tasks by tag, due date, assignee, etc.
Pro Very flexible
To-do lists often need to be grouped and regrouped for clarity. The outline-based nature of Checkvist makes it easy to move things across categories, to increase and decrease priority, etc.
Pro Smart parsing of items
Parses markdown, html links, hashtags to become formatted text, clickable links, and tags, respectively.
Pro Generous set of free features
Checkvist offers many free features if you are using this individually.
Pro Supports comments on tasks
Any item can have a free-text comment, which can be shown or hidden as desired.
Cons
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.
Con Limited capability in the android app
Checkvist is primarily a web interface.
