(This page compares the widescreen tape to a full-screen tape, both from Paramount Home Video.)
An early scene. Notice that so much is cropped in the full-screen version that it's tough to tell that the shot is actually of a reflection. Only in the widescreen version can you see the back of Jean Luc's bald skull and the window frame on the left.
And yes, in the full-screen version you even get less of the special effects.
The full-screen version of First Contact is very cramped.