I only use the same kind of glass carriers for my printing, on a very odd occasion will I use the plates without glass.
I never thought to check if there was a difference between the two.
I would check the bottom of the negative carriers, glassless and glass, to see if there are any differences.
For example on omega carriers there is a small alignment plate held down with four small screws. I have found that if one of these screws comes off the pressure is different when sitting in the negative carrier stage.
I would align your enlarger each time you change carriers as this alignment tool is quick to use, I know this solution is a bit of a pain. but other than different pressure from the bottom of the negative carrier I do not know what could be giving you this difference. 1/8 of an inch spread over a 20x24 will give you soft edges.