When power fails during a GNU/Linux operation, it will take a very long time checking that all filesystems mounted at the time of the "catastrophe" survived in a healthy state. Sometimes one or more of the filesystems are not healthy and the system will cure them. However with modern journalied filesystems the checking time will not be as long as before.
When power fails during a Windows operation, it will also take a very long time to check the disk. But Windows is much more sensitive to these "catastrophes" so it is possible that after such a crash it will refuse to boot or it will behave abnormally. Especially the proprietary filesystems such as NTFS are sometimes so fragile that they may lose all their data when the power failure appears at the right time.
All these nasty things happen even if there is no activity in the system. Including the occassional filesystem corruption (!!!).
However when power fails during the OSHS operation, the OSHS will check filesystems only if the failure occured during a writing operation. Also only those filesystems on which the system was writing when the "catastrophe" occured are checked. The other filesystems are not checked. Why? The system knows that they are in a healthy state. So you can turn your power button off when the OSHS is idle and nothing bad will happen with it (although it is recommended to shutdown the OSHS before removing the power).
How this is possible? By the OSHS feature called "transparent unmounts". When no writing activity occurs during certain amount of time, the system writes data to the disk and updates the filesystem's superblock as if the filesystem has been unmounted. However the information about the filesystem are not forgotten so when next writing operation onto the filesystem is requested, the filesystem's superblock is converted back to mounted state before the actual writing operation starts. After the writing operation is completed, it is converted back to unmounted state. Reading operations do not induce the superblock of the filesystem to be switched to "mounted" state because unlike the UNIX, the OSHS does not support access times and thus does not need to write onto the filesystem when someone requests only read access. All this is done transparently and the performance penalty is really minimal.
Even when this transparent unmounting feature is turned off, the filesystem checks will show little or no problems with the filesystems after a crash, if the crash happened in the "disk write idle" time.