In modern OS's apps don't have to be sliced in to find out if they have to do something.
I'd say that the majority of the time, background apps are asleep, awaiting either user input, incoming data, a wakeup timer, or some other system-initiated event. In other words, they take up nothing but memory until a desired event occurs.
Obviously active apps, such as music players, are a different case. But even the iPhone has a background music player, active fetch/push email app, etc, and Apple hypocritically doesn't talk about how they use up battery.
This is very true. When Apple was talking about background apps killing off battery life on the iPhone and on competing phones, they were looking at instant messaging applications.
I believe Apple said they allowed the AOL Instant Messenger to run in the background to test it's impact on battery life.
The fact is, that plenty of background processes run on the iPhone. And it is not the act of running in the background alone that kills the battery for IM applications, it's the fact they have a TCP port open, which leads to near continuous use of the radio transmitter -- it is this that is killing the battery life.
Blackberrys have a bit of an advantage over the iPhone with the proprietary Blackberry Internet Service, which allows detached and idle ports, which are handled by the BIS gateway at the provider. So if you have Yahoo messenger running on a Blackberry, it does not need to constantly maintain the port connection... but rather the port connection is handled by a proxy in the BIS gateway, and information is forwarded back to the Blackberry on a push-like basis.
The iPhone on the other hand, manages a very real TCP/IP stack over the HSDPA network. Which is cool. But it means that an iPhone or other similar offerings like Android or the Pre must maintain port connections from the handset itself. This results in much higher RF activity, which really kills the battery.
RIM sort of anticipated this problem years ago with their BIS gateway technology, which significantly reduces the amount of RF traffic a background IM client on a BB will use (by about 90%+ actually).
This is why I could have both Yahoo! Messenger and GTalk open on my old CDMA blackberry 100% of the time, and only charge the battery every two days.
If I did the same on the iPhone, WinMobile, PalmOS, or Android.. the battery would be dead in two hours.
It has nothing to do with processing power being used. It's all about the RF traffic. And RIM has a proprietary solution between it's handsets and the providers to abate the problem. All the other platforms use in-the-clear networking--which people brag is superior and more of a true internet connection--which comes at the cost of battery life.
With something like the iPhone, the problem is... power usage is not directly proportional to the amount of data transferred; sending a byte of data after second is probably going to use as much RF power as receiving a constant stream of data, because of the TCP/IP management overhead... the transmitter needs to send/receive a lot of boilerplate network traffic.
As far as I know, the Blackberry platform is the only one which has a solution for this problem. But as I said... it's proprietary and requires that the mobile provider have a BIS gateway configured on their network, specifically for Blackberry users.