There is a fundamental difference between well written Android applications and iOS ones. iOS apps are expected to run as an island. Everything they want to do should be included into the binary. There is essentially one entry point (a main() equivalent). Think of it like a statically linked binary (which it mostly is).
Well written Android applications are structured like mashups. There is no main. There are multiple entry points for screens (aka Activities) as well as entry points for processing (Services), data (ContentProviders) and even a mechanism (BroadcastReceiver) for telling all interested apps about events (eg battery charge level changing, incoming calls, apps being installed). There is a mechanism for decoupled communication (Intents) which allow specification of a verb (eg VIEW, PICK, DIAL, EDIT) and one or more bits of accompanying data (eg text, urls, images). It is trivial to bring up/use part of another app that didn't even exist at the time yours was released and have the experience combined. (You can always tell iOS apps ported to Android because they don't do mashups or collaborate with the apps already on your system.)
This means that an iOS app will never be improved by other apps installed on the system, while Android ones can be. And because of Intents it becomes possible for a user to choose their own experience - want to use a different browser or app for viewing images? No problem. For example I installed the GitHub app on Android and it added itself to the AccountManager. Now other apps can collaborate with it (eg it supports the SEND verb which creates a Gist) or ask it to display an issue/user/commit.
The (long winded) point behind this is that app installations are far more valuable to Android users. If things were only decided on technical merit then Android will end up nailing iOS because of this. But that walled garden sure looks nice to many people, and it is rare for users to really notice what is going on and they definitely won't have both devices to continually contrast and compare.