My to-do/reminder needs are fairly simple. After trying a bunch of web-based services (Todoist, Wunderlist, etc.) as well as Things, I had mostly settled on Apple's own Reminders app. I don't need to assign my reminders/to-dos to categories or projects, or give them a bunch of tags, or put them through complicated workflows and states. I just need to be able to enter them quickly, get reminded, then close them out when I'm done.
With those needs, Reminders was mostly getting the job done. My main complaint was that assigning a day and time to a reminder (or updating it later) is pretty clunky.
Due, on the other hand, has a very nice UI for both adding and updating date and time to a reminder. The entire interface is quite well thought-out and quite pleasant to use. I suspect hard-core GTD zealots will find it lacking, but if that is not me.
The app allows syncing between devices via either iCloud or Dropbox. I am using the latter, and have run into no issues. There is also a OS X version of Due, but I have yet to try it.
After a month's worth of daily use of Due, the only aspect of Reminders that I miss is the ability to share to-do lists with other people. That is a bit of functionality we use around our house that I can't replicate in Due, so I still have to go back to Reminders for the shared to-do list. It is a gap I am willing to over look, though.