A Bronx Tale was probably shot in Academy then masked to 1.85 for theatrical. So the 4:3 version doesn't lose much on the sides, only gaining extra space and showing production gaffes (ala boom mikes) not meant to be seen.

The HBO release is 16:9 anamorphic (double checked, its 4:3 letterbox 1.78:1; fucking HBO Video!!). But being an early DVD mastered from the laserdisc source, its not pretty looking combined with poor compression methods. The Universal DVD is made from a new(er) master and is believed to have its grain structure intact (not released on BD by them in the states as of yet).

Then, like you said, there's the SC BDs which are from the UK prints which have been subject to DNR.