Matt Birchler has a great camera comparison between the iPhone 6 Plus and Moto E giving us a good idea of how well a budget smartphone camera can compete with those of flagship devices.
It's obvious from the photos that the iPhone takes much better pictures in every respect, but those produced by the Moto E are respectable from a phone that costs just $60.
This part is the most important for me, though:
The Moto E takes decent pictures, but it only really works in great lighting and if everything stays perfectly still. There is also a longer delay when opening the camera app, so getting that perfect shot requires more preparation than you typically get in real life.
One of the best parts about the iPhone's camera, in my opinion, is how quickly it can be accessed (from the lock screen, Control Center or the homescreen app icon), focused and used to snap a picture. There have been countless occasions where family members with budget phones have wanted to quickly photograph a precious moment only for it to pass because they couldn't get their phone camera ready in time.