Which sync method should I use?

TLDR; Dropbox is the recommended sync method.

2Do supports synchronization between multiple Macs, iOS and Android devices running a copy of the app. With sync set up, your lists and tasks will appear on all devices without any extra effort on your part. 

2Do supports a number of popular cloud sync solutions: Reminders (iOS 12 and below), Dropbox, Toodledo and CalDAV (most 3rd party servers are supported). There are, however, a set of caveats with each of these sync methods. The main problem stems from the fact that 2Do supports far more properties / meta-data for a task than any of these cloud solutions. Things like Tags, Smart Lists, various Recurring options, Alerts, Embedded sounds and pictures are the kind of extra information you can assign to your tasks in 2Do, but not all of this data is supported by Toodledo or CalDAV for example. You can find out more about each sync method and its associated caveats in the following sections:

Sync using Dropbox (Highly recommended - for rock solid, problem free syncing)

Advantages

• Supported by iOS, Android and macOS.
• Supports multiple devices syncing using the same Dropbox account without hiccups
• All List Groups, Lists, Smart Lists, Tag Groups, Tags (including Paused), Tasks along with their attachments will sync across to other devices running 2Do. (Note: List Groups and Tag Groups are currently only support by v3.0+ on iOS and v1.5+ on Mac OS).
• Fast, automatic sync in the background
• Dropbox sync is based on our own cloud sync solution and is extremely reliable, problem free and will sync all your data without any 3rd party constraints

Caveats

• Dropbox does not have a web-interface for managing tasks. This really isn't an issue if you only ever use your devices to manage and sync your tasks.

Sync using Reminders / iCloud (over CalDAV)

Warning: Reminders no longer syncs over CalDAV starting with iOS 13 / Catalina. Read more here.

Advantages

• Supported by iOS, Android and macOS
• Your lists and tasks from the Reminders app (on iOS or Mac) will automatically sync with 2Do (with exceptions, see caveats).
• You will be able to create tasks using Siri on iOS (iPhone / iPad / iPod)
• You can access your synced tasks online using a browser (www.icloud.com)
• Syncing is Fast, and 2Do will automatically be able to perform sync in the background or at various intervals
• Your lists and tasks will sync with any other client connected to your iCloud CalDAV account
• Pictures and audio notes from 2Do will sync across to other devices running 2Do
• Multiple alarms on a single task in 2Do will sync across to Reminders as-is

Caveats

• There are limits to the number of tasks and calendars you can store and create in Reminders, which can be easily exceeded if you do not have periodic deletion of completed tasks switched on in 2Do (which is OFF by default).
• List Groups from 2Do will NOT sync across to other devices running 2Do. You will have to manually re-create them.
• Tag Groups will NOT sync across to other devices running 2Do. You will have to manually re-create them.
• Paused tags will NOT sync across to other devices running 2Do. You will have to manually pause them on other devices.
• Smart lists from 2Do will NOT sync to the Reminders app (on iOS / Mac) nor will these sync across to other devices running 2Do. You will have to manually re-create them.
• Tags from 2Do will not appear in the Reminders app.
• Unused Tags and Tag Groups will NOT sync across to other devices running 2Do.
• Unused Locations will NOT sync across to other devices running 2Do.
• Audio and picture attachments in 2Do will not sync to Reminders or to other devices running 2Do.
• Projects and checklists from 2Do will appear as simple tasks in Reminders but will, however, sync as projects and checklists to other devices running 2Do.

Sync using Toodledo

Advantages

• Supported by iOS, Android and macOS
• You can access your synced tasks online using a browser (www.toodledo.com)
• If you have a Toodledo Pro / Plus account, your projects and checklists from 2Do will sync as projects and checklists to Toodledo
• Use email to create tasks and sync with 2Do. Toodledo gives you a unique email-address to which you can email tasks. This allows you to add tasks to Toodledo (and thus to 2Do) from any email client. You can even use Siri to compose these emails for you.
• Tags will sync from 2Do to Toodledo
• Repeating tasks will sync to Toodledo

Caveats

• Automatic background sync is not available as an option. You will have to click on the Sync button each time you wish to sync. This is because Toodledo puts a limit on the number of times a device can sync (along with the number of tasks that it can sync at one time) and will suspend the account if it's syncing too often. If automatic background sync is important to you, please explore the other sync options such as Dropbox or iCloud.
• List Groups from 2Do will NOT sync to Toodledo or other devices running 2Do
• List colors do not sync across devices. 
• Smart lists from 2Do will NOT sync to Toodledo
• Projects and checklists from 2Do will appear as simple tasks in Toodledo if you don't have a Toodledo Pro / Plus account but will, however, sync as projects and checklists to other devices running 2Do
• Only tags assigned to a task in 2Do will sync across to Toodledo. Unused tags will not sync.
• Paused tags will NOT sync across to other devices running 2Do. You will have to manually pause them on other devices.
• Audio and picture attachments in 2Do will not sync to Toodledo or to other devices running 2Do
• Alarms from 2Do will not sync to Toodledo
• Emoji UTF-8 characters cannot be used in task titles or notes as Toodledo does not support them.In fact, ToodleDo will replace Emoji characters with question marks, and all tasks that had an Emoji will be duplicated: one will have the Emoji, the other will not.