I have many friends and colleagues that believe swiping away all your applications saves power. They’re wrong. Depending on their phone.
iOS applications are purely interactive. When they’re not on-screen, they’re shut down, frozen, not receiving any input from you, not doing any computations, and with a few exceptions, they’re not even interacting with iOS itself. iOS keeps your frozen applications in memory until it needs that memory for other things, but that’s not using any more power than if the apps were not there — the memory still has to be powered. iOS itself has operating-system processes that run in the background, but not user/app-launched processes.
Contrary to what many believe, forcing iOS to unload an application will actually take a tiny bit more power, since iOS has to run the routines required to shut the application down. And it you run it again, it’ll have to load from flash memory, again using a tiny bit more power than if it has just remained frozen in RAM.
On Android, there are several kinds of programs. There’s the basic application, which similar to apps on iOS, is shut down in various ways when not being used interactively (not on-screen… Android can run multiple apps on-screen). Just as in iOS, these applications are shut down in several stages by the OS, they’re frozen in RAM, if Android needs more memory, it’ll unload an App or two, but otherwise, they’re best left in RAM.
However, Android also has a thing called a Service, which is essentially a background program that runs independently of user interaction. Some applications launch their own services that run in the background and can use varying bits of CPU and/or radio power. So when you fully shut down an application on Android, you’re shutting down any Services that application has previously launched, and perhaps saving a bit of power. It’s also technically possible for a Service in Android to abuse this and draw lots of power. Android actively tracks the use of power and other resources, so these are discovered fairly fast.
minutiae 