Both smartphones support Microsoft Exchange contacts, emails, tasks, and calendars, as well as email in IMAP, POP, and Gmail accounts. (Android supports iCloud email, as iCloud uses IMAP.) iOS does not support Google contacts directly, but it does support Google calendars. Android of course does not support contacts and calendars in Apple's closed iCloud service, though you can get apps that bridge the two.
Where iOS really shines is in its support for Gmail and IMAP (including iCloud) notes, a feature I rely on immensely. If I add a note on my iPad, Mac, or iPhone, it's available to every device immediately. Android doesn't even have a notes app, much less a cloud-connected one. The Galaxy S III does include Samsung's own S Note, which lets you create text and graphics in your notes. But it's more work to use than Apple's very simple Notes app.
iOS also offers the Reminders app, which is frankly too primitive (no shared task view, for example) for serious use. It does have the ability to set an alert based on when you arrive or leave a location. Android has no tasks app.
All in all, the iPhone 5 and Galaxy S III are close in this category. iOS holds a slight overall edge due to its notes and task support, but if you're an appointment junkie, you'll prefer the S III.
Another area where Android has come a long way is apps. The selection in Google Play is now quite large, especially for content-oriented apps and gaming. It's also easier now to buy an app on your desktop and send it to your Android devices. But some apps aren't compatible with all Android devices, given the wide range of Android versions and other customizations in the Android universe. Version compatibility is an issue with iOS, as well, but much less so. If you buy an app for iOS, you can get it instantly on all your devices -- no need to install on each independently.
There are more, better apps on iOS related to business productivity. For example, Android has just Quickoffice and the weaker Documents to Go. iOS has those two plus Apple's solid iWork. (The productivity app selection for the iPad is even better.) There are many great apps for photo editing, drawing, music editing and creation, and so on in iOS than in Android.
Both the iPhone 5 and the Galaxy S III support dictation, as long as you have a live Internet connection, and both have a voice-based assistant. Apple's Siri service on the iPhone 4S, iPhone 5, and (if you're running iOS 6) third-gen iPad responds to questions and can take actions based on your voice commands.
Sign up for CIO Asia eNewsletters.