In the matted theatrical presentation of
The Shining you would not have seen the helicopter blades in the opening shots because they would have been cropped. The film was indeed shot with the intention of it being shown in a scope-like format, but apart from a couple oddities the filmed material looks equally good in standard.
Example of a soft matte (taken from
How Film is Transferred to Video):

Here it seems that we really lose picture information with the letterbox version: There is clearly more information on the top and bottom of the screen in the open matted version. Unfortunately this extraneous information is also the problem of opening the mattes. The areas now opened for the viewer can't have important new information compared to the letterboxed release, because the director was only looking at the widescreen area shots when he was making the movie. There also may be some unwanted information present in the opened matte like in my example picture: a microphone at the top of the picture and a Coke-bottle at the bottom of the Enchanted Sea. These days, though, this is not such a problem anymore, because when making the video master, the picture may be zoomed into in critical scenes where unwanted things are shown.
For economical reasons, special effects are usually shot or calculated only for the widescreen part of the movie (typically around 2:1), so in scenes with special effects a full-screen version of an open matte movie is panned & scanned just like an anamorphic or hard-matted movie. This can clearly be seen in
Terminator 2 or the
Back to the Future movies.