SwiftKey keyboard has the swype down short cut that you want and to bring it back up it is a tap in text area.
HTC keyboards have a little icon on the left to drop the keyboard down. Some phones also drop it if you tap the Menu key.
But overall it comes down to what's been said since day one, iPhone is just a better experience.
For you, sure. Other people can have different needs, wants... and histories.
It's a well known phenomenon that user preference often comes down to the type of UI a person learned on first.
For instance, people who started with a dedicated Back button often miss it when it's not available.