How useful is the feature to double-click the home button to bring up the iPod controls from anywhere on the iPhone to you?
Take that metric, multiply by the number of apps you have on the phone, and that is how useful multi-tasking will be to you.
Multi-tasking is about more than saving state in an app, switching apps faster, and running apps in the background.
1) Saving state can be a nice feature, but it isn't appropiate for every app in every situation. For example, Settings should almost never save state. You don't wan't to always have to navigate backwards to change a different setting than that which you changed last time, do you? On the other hand, if you are in the middle of setting up a mail account you don't want to lose your place if you need to switch apps.
Another example for me is the USA Today app. When I open it for the first time that day, I want it to start at the main page as if I were picking up a new paper (which it does). Alternatively, if I want to google some information or copy/paste content from the article, I want it to keep my place in the article while I switch apps. Currently, the iPhone can't distinguish what behavior I would prefer since there is no differentiation betwen closing an app and merely switching to another.
2) It is more than just switching apps faster, although that is nice. If you use the double-home-button-click for iPod controls feature, what makes it so useful? How is it different than just closing your current app and switching to the iPod?
It is about preserving your train of thought. When one app launches another on the iPhone (like loading an address in google maps), what happens when you close that secondary app? You don't return to the original app, you start from scratch at the home screen. Why do you think apps started including their own bundled (safari) browsers? When you switch to another app, you put your train of thought on pause and start a new one. It is easiest for our minds to recall the original train of thought when he have clues - switching back to an app as opposed to continually re-launching from the home screen.
Why do you think tabbed browsing caught on so well? If you come across a new subject while browsing, you can open it in a new tab. When you are done exploring that topic, you can simply close the tab and you immediately return to your original train of thought. As your short-term memory manipulates all the information you take in from the secondary tab, your original train of thought associated with the original tab is moved to long-term memory. When you close the secondary tab, the information associated with the first tab must be moved back into short-term memory from long-term memory. It is much more efficient to do so when your brain has cues - in this case the first tab which holds the last page from your original train of thought.
It feels much more natural when an application stays open when switching to another app because when you close the second app, your first app is immediately available, right where you left it, allowing your brain to recall that train of thought without missing a beat. It's not as fluid when you always return to the home screen.
