Her location-based and people-based reminders have been a killer feature for me. I can open Cortana and say "Next time I talk to my mother, remind me to ask her for her cheesey corn recipe". Then, next time I open the messaging app to text my mother, or open the email app to email her, or when the phone's GPS realizes I'm over at her house, Cortana will show that reminder[3].
It also works for location-based reminders: "Next time I'm at the hardware store, remind me to buy softener salt". It's been about six months since I've last used Android, but I don't think Google Now could do these types of reminders when I switched.
[1]. Two other reasons: I much prefer "Live Tiles" to widgets or app buttons, and the Lumia line's cameras blow most other phones out of the water.
[2]. According to the /r/WindowsPhone subreddit, Microsoft tends to update their apps on Android and iOS long before they update them on Windows Phone. Additionally, apps on the other two platforms tend to be more feature-complete. This is all anecdotal though, so take it with a grain of salt.