A conventional cup and cone BB will almost always be lighter than a cartridge BB, unless you are comparing a very low end cup and cone BB against a very high end cartridge BB, and even then the cartridge BB may be heavier (carbon spindles don't count unless both BBs have the same type of spindle).

The spindle length is dependent on the combination of the frame AND the crankset you are using. The chainstays may be bent, flattened, and/or ovalized, and that can affect how much spindle width you need for the inner chainring and the crankarm to clear the chainstays.

What I do is install a BB and the crankset, then check for adequate clearance of the inner chainring, and the crankarms, and then last check the chainline to see if changing the spindle length is necessary or desirable to improve the clearance, or the chainline.

Clearances FIRST. Because without adequate minimal and proper clearances, who cares if the chainline is what the manufacturer recommends or not, you will not be rotating the cranks anyway.