I've been trying out a new delivery tracking app recently called Parcel, and it's been absolutely fantastic to use. And while it's a lot simpler than the popular Deliveries app, it does a few things that for me, make it a much better choice.
One main annoyance I had with Deliveries, was that Royal Mail (the main postal service in the UK) deliveries weren't supported properly. You could add them, but it would just redirect you to the web if you wanted to actually view the details. Fortunately, Parcel supports Royal Mail deliveries like any other, which makes it instantly better.
That's not it though as Parcel can also automatically track Amazon orders, which is incredibly useful. And while it's not automatic, there's also support for Apple Store orders, just use the order number and Parcel can fetch all the details.
So while it may not be the most feature packed app, or have the most custom design, I think it's fantastic.
If you want to try it out, then Parcel is free on the App Store, and if you want to track more than three deliveries at once and also have push notifications, then the premium subscription is just £2.99 a year.