In my experience, apps crash less and are less buggy in some ways.
I have a galaxy note 3, and my bro has a iPhone 6 plus.
App sharing seems to be getting better, as others have pointed out, but it's obviously not perfect.
Another nice thing about it is that you can use it like a USB and have a file manager.
Google Apps on iOS are definitely prettier and more feature rich than on Android in some ways (or all). But the 2 hour try/refund policy is neat, and not having to type in a password for every free app that you download (although I understand that kids can be annoying) is neat, the 15 minute do not ask option aside.
Things are lot easier to touch on Android, even with a bigger screen size, as I feel as though I have to use the edge of my fingers.
Back to kids, you can set a passcode on every single app, and even on the multitasking screen (just not the notifications hangar or whatever the fuck it's called), which helps when giving your phone for people to use and play games on, although I have it mostly off since I don't share my phone, and lollipop has "profiles", not that a lot people have it, that you can protect with your lockscreen password, etc, and lend your phone if someone wants to make a call or whatever.
I can also adjust different volume levels within a few clicks, instead of worrying about not being able to change anything or move out of apps, should my phone guess incorrectly. The lack of silent mode is annoying in lollipop (not that I have it) and I love using the silence switch when I'm playing games on my brother's phone.
Although it's limited to phones without a locked bootloader that also might not have a monthly payment plan system (credit cards aside, I guess), you can flash a custom ROM that allows you to have a "better" OS, compared to just rooting or jail breaking your device.
The keyboards are much more feature rich than the same apps for iOS are, plus I get to use Google's text to speech and not SIRI (or Siri). E.g. SwiftKey for Android is better than SwiftKey for iOS. You can write app reviews with different keyboards, either, which sucks.
Widgets are a plus, but can be limited as it seems like developers have forgotten about them, or that I don't use enough launchers that make some to use my own.
Have multiple launchers available is debatable, as people have their own preferences and find the basic one that comes by Google as confusing, although I could see how I can suck in some ways. But simply being free to remove and position icons anywhere is neat. Practicality over design.
My nose will suffer a fracture if I drop a metal iPhone on it instead of the cheap plastic that comes on Android when in bed.
I'll add more as they come along.