First and foremost, Apple needs to look at how Android's notification shade handles access to commonly-used settings. Apple's current solution, Control Center gets the job done for some things, but I would wager that most people don't use it as often as Apple would like.
Android N's shade is so nice for three big reasons:
1. Customizability is king. Different people need access to different settings more often, so being able to customize what ones show for you, and in what order is a big perk. Take a look at how often I use the 5 settings Apple give me quick access to in iOS 9.
For all intents, that is basically wasted space for me. Let me customize how these controls are laid out, please.
2. Double tapping one of these icons takes you to it's page in the phone's settings app. iOS 9's Control Center lets me turn these features on and off, but if I want to do more I have to get out of Control Center, go to the Settings app, and find the setting I want to dive into. Having the ability to tap once on the WiFi icon to turn on/off is convenient, but being able to double tap it to hop right into a list of all available networks is great.
3. Simplicity. Ironically, while Android has a home screen that lets you put a bunch of crap everywhere, has a much more simple layout for it's quick controls. It's just a line of icons if you pull down from the top of the screen. Need more controls? Pull down again and you get a grid of all your options.
The other thing I really like about Android N is the ability to double tap the multitasking button to switch immediately to the last app you were using. This enables you to bounce back and forth between 2 apps incredibly quickly, and without seeing the multitasking screen at all. This one can't be described that well in writing, so I'll just let MKBHD do it for you.