Apps are the current killer-app. Sounds funny, but from "app for that" commercials down to blogs keeping running tally of which platform has how many (100,000+for iPhone vs. 10,000-ish for Android if you're curious), arguably nothing is supposed to matter more to consumers right now.
To be fair, not all those iPhone apps are what we'd call hight quality. Apple's mature, well polished Xcode and Cocoa touch development and iPhone SDK makes it easier to build iPhones apps - maybe too easy at times. By the same token, not all the Android apps are exactly golden either.
DROID's advantage is that Google offers a more open development environment, meaning they don't moderate their marketplace the way Apple does the App Store. Developers are free to make and upload pretty much anything they want, and only if there is a complaint will Google investigate and potentially remove it.
Also, developers can provide "side loading", or apps that can be installed outside the market. This may appeal more to pro-level or geekier users, but it should be a consideration for everbody.
Apple only allows apps that Apple approves into the App Store (and limits side-loading to 100 "ad-hoc" seats, or custom Enterprise deployment). While this should theoretically make for a "safer" environment, the capricious nature of what's accepted and what's rejected really just makes it more frustating. Again, for geeks. Most users, however, will never notice this. With 100,000 apps, chance are you'll find what you want never notice what makes all the bloggers crazy. It's just not a consumer issue.
Apple's iPhone only lets the built-in apps like Mail. SMS, Phone, iPod, etc. run in the background. So, you can listen to music on your iPhone, or streaming via Safari or iTunes, while you use most other apps (even the phone), but you can't do likewise with a 3rd party app such as Pandora. The iPhone does implement "push notification" to alert you to activity in Instant Message clents and other apps. It works in most cases, but lacks Android's more sophisticated nofication management as well.