For Personal Use

Here's how both of these stack up with personal task management.

Todoist

When it comes to personal use, Todoist is a really nice all-around experience and presents a good way to start adding tasks, assigning them to a day using natural language input, and organizing them into a project. Inside of that project, you can organize those tasks into a board view or, more recently, a calendar view to express what's coming up.
Now, Todoist has a wide range of custom view abilities, which are a real help in fine-tuning how you want each of your different areas to look. For example, inside of Todoist, if you're looking to plan your time ahead for the week, including all of the tasks that you do for work and life, then it is a great option to go to "Upcoming," which will allow you to see that in a board or a list view for all of the tasks that are coming up in your work list. This is perfect for looking ahead and managing what you want to do.
Now, Todoist also has lists where you can organize your tasks into them. Both of these applications have fantastic mobile applications, which allow you to capture tasks really quickly for day-to-day management. Todoist also has an inbox area, which will allow you to see your captured items and organize them into the correct areas.

Any DO

Any.DO is really popular for personal use because it organizes your list as a very visual canvas and has a clean user interface, allowing you to add items, including tasks, which make it perfect for not just your work but also grocery lists, movies you want to watch, and a wide variety. This is why 40 million people are using it, and it's becoming very popular among families for organizing ahead. One of the standout features for personal use is the calendar abilities.
This has long been available in Any.do and has had this feature for a very long time, allowing you to see all of your events that are potentially in Apple Calendar or on Google Calendar, and be able to see them alongside your tasks. For a lot of people, this is probably the original daily planner application that allows you to see what's ahead and start working on tasks.
It also has a killer mobile application, which a lot of people like for iOS and Android, with great widgets to see what your events and tasks, as well as conference calls, are coming up, and reminders for time-based locations and recurring reminders as well. It also has good sync, which means you can get it not just on all of the mobile devices, but also on your Apple Watch and Google Wear devices.
Todoist also has a great personal feature, which is WhatsApp integration with Any.do, locked under the premium. This will allow you to communicate with Any.do and manage tasks and reminders just from using their WhatsApp chat function, which is much more of a time-saver when going about your workday.

Todoist vs Any.DO: Comparison & Breakdown