The Apple ecosystem is inherent to its devices, just like Google's, Microsoft's, and Blackberry's. In that sense, it's better. Remember, some things are exclusive to the brand. iMessage and FaceTime, for example.
I don't agree with that.
iOS is locked down and that's why 3rd party alternatives are worse than on their native (and other) platforms. This is not the case on Windows 10, where you can simply uninstall Microsoft Office and install WordPerfect Office and it works just as well. Or you can change iTunes to the default media player, and it works about as well as on macOS.
On iOS, these simple things are impossible, so you end up with good service and apps having poor user experience in day to day use on iOS. The result of this is that many users are frustrated into just using Apple's offerings, because even disabling them won't rectify the situation - it will just break the system (as the OS is hardcoded to work only with their apps in many places).
Cortana for Android is almost as good as the Windows Phone version. It's the vector through which Microsoft is implementing all of their Continuity/Handoff features between Android and Windows 10. This is literally impossible on the iPhone because Apple has made it so.
It has nothing to do with the fact that Microsoft develops Cortana and they own a platform (Windows 10). The ball is in Apple's court.
The reason why this is so, is because the business models are different.
Apple is a hardware company, who provides software out of necessity, to avoid being marginalized. This also allows them to design their systems in a way that bias them towards each other, to get consumers to buy more Apple hardware and have no way to replace them with non-Apple alternatives. So, Apple has a clear rationale for WHY they should made the alternative software/services as awful as possible on their platforms (which run on their hardware), and get users to use as much of their own technology as possible (which typically is only available on their platforms, which runs on their hardware).
On the flip side, Microsoft and Google are Software and Services companies, who do devices for reference and trend-setting purposes, and out of need when OEMs are slow to approach specific markets (they will take the risk first). Because consumers or software and services are their biggest "want," there is no rationale that involves gimping their software or services simply because it's running on something that isn't Windows/Windows Mobile or ChromeOS/Android. Their business models are built around people consuming or buying their services or software.
This is why Microsoft users complain about Microsoft Mobile software being so good on iOS and Android, and why Google users complain about their support for iOS - while iOS users could never do this... Because those companies go out of their way to make the 3rd party experience as good as possible - equal or better to the 1st party experiences when possible.
The only thing that stands in the way of that is Apple.
Compare Cortana on iOS to Cortana on Android. I doubt Microsoft is gimping the iOS version simply "because they can."