When comparing GTDNext vs Turtl, the Slant community recommends GTDNext for most people. In the question“What are the best cross-platform task apps?” GTDNext is ranked 13th while Turtl is ranked 15th. The most important reason people chose GTDNext is:
All the “Get Things Done” lists you would expect: next actions, someday, waiting, and scheduled.
Specs
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Pros

Pro GTD style lists
All the “Get Things Done” lists you would expect: next actions, someday, waiting, and scheduled.

Pro Automatic next actions
When it comes to choosing your next action, most to-do apps suffer from the same problem: All of your actions (sometimes hundreds in total) are visible to choose from. This can overwhelm users and cause them to give up on the system. GTDNext is different. In the "Next Action" view, only the very next action is shown for each of your projects. This results in a nicely consolidated view of only the things that need your immediate attention.

Pro Unlimited levels of projects and actions
In GTDNext you can set up an unlimited number of levels for your projects and actions, allowing you to plan your project and sub-projects in as much detail as needed.

Pro Areas of Focus
GTDNext supports the “Areas of Focus” methodology from Getting Things Done. You can filter all of your tasks to just show your work tasks, side project tasks, or personal tasks. There is also a global filter, so that when you’re hard at work you can focus only on your work projects and tasks.
Pro Option to visualize all projects and tasks in a single outline view
This is really useful because it prevents you from having to navigate through each project individually.

Pro Many keyboard shortcuts available
The number of keyboard shortcuts makes it easy to log or add tasks without removing your hands from the keys.
Pro Multiple Platforms (Windows, Linux, macOS, Android, Firefox, Chrome)
Turtl has applications for all the major operating systems, as well as Android. In addition, there are extensions available for Firefox and Chrome that cooperate with the downloadable applications.
Pro Open source
The app is licensed under GPLv3 making it open source. This means that anyone can use the code and contribute. This also makes it easy to use on one's own server or for company solutions.
Pro Good security
After assigning a password to your account in Turtl, a key is created to encrypt the entire account. No data is stored on their servers meaning they have no access to unencrypted content. This is a huge leg up when comparing to other Evernote alternatives.
Cons
Con No mobile app available
Con Web only
GTDNext does not have native apps for other devices, but it does work across PC/Mac/Linux on the web client.
Con No Google Tasks integration
Con No iOS app
While many other operating systems have a client, iOS does not have one yet (though it is planned).
Con No image embedding
Instead of image embeddings, there's a sort of poor man's substitute: image + description. If you add an image, you can create a description of any size and with all the formatting features. It can be used instead of image embedding but much more limited: only one image and only at the very top.
Con Internet dependent
Requires Internet connection to initiate offline mode, loses access to notes without Internet or server.
