Hands down the two best things about voice assistants are that they allow you to speak you query or instruction in the kind of Sci-fi computer interaction that 60s era Star Trek saw as the future; and that they are so deeply integrated into the phone as to make their use as friction free as possible.
The best implementations require no physical interaction with your phone. The Motorola X, Lumia 930, Galaxy S4 (but not S5 or S6 bizarrely) and iPhone (when plugged in) allow you to call out to your locked phone and launch Google Now, Cortana, S-Voice or Siri. It is the future and when you've had that capability anything else seems kind of clunky.
So Cortana will be making the jumps from Windows Phone to Android and iOS as part of Microsoft's strategy to be on everything, everywhere. Most observers agree that Cortana is the leading voice assistant in terms of capability. However distilled down to an app that needs to be manually started after first unlocking your phone it seems to me that much of that advantage will be lost. Yes, you'll still get the time-based notifications and possibly the location based ones too.
What you won't get is the seamless, friction-free experience which makes Cortana so useful.