First, just a few small points/corrections.

The film (and a majority of films made since the mid-1950s)was shot for 1.85:1 (not 1.78:1) 1.78:1 is the ratio of a Widescreen-TV.

The ratio of the 'uncut' picture was (I think) 1.37:1 (most TVs use a ratio of 1.33:1) This is the same ratio used to shoot just about every movie since the 1930s.

In fact, most 1.85:1 films are shot this way (evidently, the shape of the 35mm film or the camera or some such thing, means that the image is invariably that 1.37:1 ratio.) However, some films use "hard matte" (which means blocking the top & bottom of the image from ever reaching the film,) while others (like The Godfather) use soft-matte (which means removing the top & bottom in post-production.

As to the question of which I think is better, I'd go with the widescreen. In the side-by-side comparison, I noticed especially that we see alot more of the ceiling in the Godfather's office, makes the place look less 'cosy' than the 1:85.1 version, my point being that added picture often detracts from the effect of a shot. Close-ups become mid-shots and such.

Now, I'm guessing that when the cinematographer said he composed the film to work in both formats, he means he composed each shot for the 1.85:1 format, but still made sure that it was perfectly watchable in the 1.33:1
(ie, made sure there were no boom-mikes on-screen and such. Many films didn't take this sort of thing into account, in fact the viewfinder on some of these cameras didn't even show outside the 1.85:1 area.))