If you don't use a password manager like 1Password or LastPass on iOS, I'd highly recommend watching the above video. It walks you through how password managers make it easy to enter your username and password into websites and apps.
Android O was announced last month, and one of the big updates is the autofill API which companies like LastPass are really excited about. LastPass on Android can already fill out some forms for you, but it's kind of a hack built on top of Android's accessibility framework. You need to go through a couple steps that aren't that hard, but is something that throws off many users to the point where they don't do it.
But let's say you give it access, then this feature does work pretty nicely. Login forms in Chrome will have pop ups that let you insert your credentials quickly, and some apps allow this. Not all apps mind you, and quite reasonably, many apps don't want other apps messing this sensitive login information. It's a helpful ability that is hamstrung by the hacks way it's implemented by apps like this.
On the iOS side, password managers have had better system-level APIs since 2014 and iOS 8. Using password extensions, you can automatically fill in not only username and passwords, but name, address, contact info, credit card, and bank account info as well. Here's a quick video showing it in action on iOS today:
Based on my reading of LastPass's post as well as the Android O developer documentation, it seems that Android O will match what iOS has today. Logins, addresses, and card information will all be able to autofill. Android O may get the edge if these autofill options display automatically when the user taps into these fields. That would be quicker than iOS, in which case I'll be jealous. Otherwise, this seems like a lot of things in Android O…Google is adding things iOS has had for years.
UPDATE: Thank you to Carlos Ribas for bringing this WWDC video to my attention where Apple shows how apps can access iCloud Keychain to make this a seamless process already. This only works with iCloud Keychain of course, so 1Password and LastPass users can't take advantage of this specific functionality. Likewise, thanks to Michael Bond for showing me Smart Lock, which is a similar feature on the Android side.