I don't know about iTunes, but Google Play gives you lots of stats about installs (Both Total, and current on active devices); as well as in depth break downs of these based on device os version, country, app version, etc.
Amazon really only seems to give you a total downloads figure.
I use my own system to monitor things like number of sessions daily, session duration, and also insights into how users are interacting with the app/game.
I guess I was just wondering if anybody else does the same, but it seems that no one does