Apple - Make Dropbox app upload in background without having to open every 10 minutes

You can't. There are restrictions with iOS multitasking that prevent apps like this from running all the time. You might be able to bypass this by jailbreaking though.

Also, apps can't bypass this on the App Store due to guidelines such as:

2.5 Apps that use non-public APIs will be rejected

^{Source: https://developer.apple.com/appstore/resources/approval/guidelines.html}

Jailbreak your phone and then download 'Background Manager' and it'll bypass Apple always killing DropBox in the background every 10 minutes. It's great because now DropBox will upload in the background or at night when I'm sleeping, while the iphone is plugged in!

Obviously, Android and iOS are two very different operating systems, with different ways of doing things. Apple chooses not to let apps run in the background forever. This helps reduce the drain on the device's battery. That being said, "Background App Refresh" has been around for a while. App devs have to add this capability to their apps. It isn't done automatically.