In the best case, the amount of resources consumed by multiple apps will be the same as when you are running a single app. In the worst case, multiple apps will consume more resources than a single app. Therefore, to stay on the safe side, you should close all background apps.
An iOS device consumes more (or the same amount of) resources when there are multiple applications running. Let
S be the amount of resources consumed with a Single app running, and
M be the amount of resources consumed with Multiple apps running. We have the following relationship:
S <= M, and closing apps will keep you on the safe side.
Although Apple's intent was for users to not have to worry about background apps, that doesn't necessarily mean that it is that way. The fact is that developers have the freedom to implement apps as they please, and once Apple opened up the App Store to any developer in the world, all bets of Apple's intent were off. Although developers technically only have 5 background profiles to choose from, there are several ways in which Apps may undesirably consume resources:
- Unwanted background behavior: E.g. A user uses Skype for IM only, and doesn't quit the app after the IM session is done. The app is listening to VOIP even though the user is not using it for that reason.
- Unknown background behavior: Imagine an app which helps remind you where you parked by using your GPS. Is it using Apple's GPS background process, or is it using some other feature? Or how about a podcast app which is playing a podcast that is in the process of being downloaded. Will it automatically remove itself from the background once it no longer needs to download the podcast?
- User error: A user is running a radio application and uses the pause feature rather than stop feature, which causes the app to continuously consume resources, but, since the music is no longer playing, has no indication that it is doing so.
- Application error: A radio app which gets indefinitely paused in the background, e.g. due to a poor connection. The user has no indication that the app is running and consuming up resources. Even this article which argues the opposite case mentions that there are apps that can go "berserk and will not terminate properly."
- Undocumented features. There have been cases where apps pass the review process even though they contain features Apple doesn't allow (e.g. tethering). It's not farfetched to imagine a developer hiding a background process in their app as well. It could easily be masked if some portion of the application actually utilizes the documented background processing feature, while the rest does whatever it pleases once it's running in the background. The main reason tethering apps are removed from the App Store is because of the publicity they generate. An application that uses background processing for undocumented reasons would be able to fly under Apple's radar for many years, since no one would necessarily know about these features, let alone care enough to discuss them on the Internet.
With over 500,000 apps on the App Store, there is no way to know what each application does, let alone know what kind of background process it may be running, and whether or not it is well-written.
This is the same reason an Apple Genius would recommend that you close all the apps in the tray. No one is arguing that all of those apps are running and consuming resources. They're arguing that some of those apps may be consuming resources, and since there is no way to know which of them are using up resources, since the icons look the same, the easiest way to solve this issue is to close all of them.
Technically, you could go through the list and ignore all those apps which you know for sure don't use background processing, but that is a far more challenging task than simply closing all of them. (Here's an example which although is exaggerated could still be real: This is a turn-by-turn GPS app, so I need to shut it off; this is a radio app, but I never pressed the play button, so it shouldn't be streaming in the background; this is a GPS app which doesn't use turn-by-turn, so I don't need to close it; this is an app which might be downloading something I don't care about, and I closed it 6 minutes ago, so it might be in the 10 minute window of bg processing, and I should close it; this is just a game, so I don't need to worry about it; this is a parking app which uses my location, did the developer implement it as a GPS app or does the GPS only work when I launch it?) Compare that with: close, close, close, ...
As the number of apps you have installed on your iPhone increase, so does the likelihood of having background processes consuming undesirable resources.
You can't expect a user to know how every app they download will behave. Therefore, if a user is concerned with unnecessary background processing, then closing apps is a good idea.
There have been many times when I would notice my iPhone getting really hot even when I'm not using it. The cause is always some application(s) which is using the processor even though it's not necessarily running in the foreground. The quick fix is to close all the applications (by double tapping the home button). So far this has always resolved my iPhone's overheating issues within a few minutes.