Based on that information there are several reasons why those you are flying with might use LVL CHG. On the 200 with the SP-177 AFDS system that was the preferred mode to use. Also on the Classic selecting LVL CHG automatically puts you in the N1 mode and is the recommended mode during engine out acceleration and climb up to software U10.7 even on the NG (U10.8 and later it is LVL CHG or VNAV).
By using LVL CHG as a standard you are using a procedure that stays the same during both 2 engine and engine out climbs. From a Human Factors point of view when you can harmonize a procedure for non normals with what you do everyday you decrease the chances for error.
Does your Company use the Boeing FCTM or a tailored FCOM Volume 1? What do the procedures in there call for? If it is not specified those you are flying with may have learned it as one of those dreaded undocumented techniques so many of us use cling to because they work even if we don't remember why!