Unfortunately, the concept of "multi-tasking" is not well understood by many consumers. Adding to the problem is that Apple intentionally obscures their version of "multi-tasking," largely because the version in iOS is both limited and simplistic.
Perhaps this will help. First, it's important to understand the difference between "running" apps and "in memory" apps. Running apps are those that are actively using CPU cycles. A true multi-tasking OS allows multiple applications to request CPU cycles and schedules the operation of the CPU to meet those demands. When an app is actually "running" it uses information stored "in memory." If the information is not available "in memory," the OS must load that information from "secondary storage." (Apple intentionally obscures the difference between "memory" and "secondary storage" primarily as a marketing choice.)
Think of "memory" as a big room with a bunch of chairs, say 50. When an app "runs" (i.e. uses CPU cycles) it needs some to access data in some of those "chairs." If it needs more chairs than are currently empty, the OS asks some of the chairs to be vacated. When that happens, the information used by non-running apps vacates the chairs and move to other chairs outside the "memory room" in "secondary storage."
Of course, if there are empty "chairs," the OS simply allows a running app to "fill them up" with its own data. In that case the OS doesn't need to "vacate" any additional chairs.
What this all means is that as long as apps "behave themselves" and vacate memory when told to do so, there is no need to "kill" an app simply because it is "in memory." As long as it's not "running," (using CPU cycles) it is not affecting performance.
A sophisticated multi-tasking OS (such as Android) will take into account how many "chairs" an app needs (when it runs) and how often the app actually "runs." It will shuffle the "memory chairs" in such a way that overall performance is maximized.
Apple's iOS is much less sophisticated (for good reason discussed below.) Rather than allow any app to request CPU cycles whenever it likes, iOS has a few "privileged" apps (e.g. Pandora) that are allowed to make such requests while other apps are running. Thus, you can listen to music while surfing the web, but you cannot, say, play Angry Birds while updating a spreadsheet. (Not that you would want to.)
All of this means that when you request an app in iOS, the OS makes decisions about which apps can continue to make CPU cycle requests and which must be "suspended" (i.e. the information about their current state is stored and the app is prevented from making further requests for cpu cycles until it is activated again.)
The basic difference between "true multi-tasking" (e.g. Android) and "pseudo multi-tasking (e.g. iOS) is that a true mult-tasking OS makes no distinction among the privileges of apps. Thus, in Android you can update your email, update a news feed, and listen for text messages (in the background) while you listen to music and work on a spreadsheet. Android doesn't care what combination of apps you ask to run simultaneously. It simply responds to those requests by scheduling CPU cycles and moving data in and out of memory.
In iOS, on the other hand, there a significant restrictions on which apps can run "simultaneously." This is an inherent limitation on the flexibility of the device. On the other hand, it has major advantages.
What it means is that, unlike Android, iOS is much less subject to "lags" as demand on CPU cycles increases. It also means that it is less vulnerable to
"badly behaved" apps that insist on making demands for CPU cycles and don't vacate memory when told to do so.
In effect, Apple decided which user tasks might be used simultaneously with other apps and granted those apps (e.g. Pandora) a privileged status. All other apps must either be running or are forced to suspend themselves when a user stops using them.
All in all, an Android device will provide a user with greater flexibility but the price is a faster CPU and more memory (i.e. more chairs in the memory room) compared to a comparable iOS device. Apple places such a high priority on consistency in response to user requests (i.e. "smoothness") that it is unwilling to allow the sort of free-for-all Android allows. Furthermore, the operating system, itself, is simpler to design and operates more quickly (for a given CPU speed.) In short, iOS need not be as "smart" as a true multi-tasking OS like Android. But it may well offer less long-term flexibility as new apps emerge.
The bottom line is that for a device like a phone, Android may be overkill. And even for a tablet the less flexible but more predictable operation of iOS may be preferable. At the same time, however, Apple has a more difficult time juggling demands from apps that want to run in the background unless they're "privileged" to do so. Android faces no such obstacles; it simply needs more "horsepower" to cope with demands of various apps.
There is no need for a "task killer" in either environment (as long as apps are "well behaved.") The Android OS is very good at allocating CPU cycles as needed (and allows a much larger set of apps to run simultaneously). But it is vulnerable to "slowing down" when that happens. iOS "solves" the problem by restricting the number of apps that are "privileged" to multi-task.