There are two ways to do multi-tasking well on a mobile device:

1) Like most current phones, suspend background applications and allow only specific background tasks (downloading data, playing audio, etc).

2) Keep all open apps in memory, but limit background apps to only tax the cpu when absolutely necessary.

Both differ very little actually on battery drain. It may even require more energy to constantly suspend and restart applications. The disadvantage of the latter is more the increased memory demands, which makes it more important to close or kill apps frequently. Less so, if the device just so happens to be stacked with massive amounts of ram...

Another disadvantage of course is, that bad apps can cause more harm to the battery while there are in the background.