I don't think they are synonyms (at least in Polish). I guess that "duża spódnica" refers to the size (waist/hips) - depending on your body type and how slim you are you could need a big or small skirt (even if you were interested in a skirt of a fixed length, say ankle length).
I have seen spódniczka used as a word for skirt. Wicktionary says it's diminutive, so is spódniczka a short/small skirt?
I would also like to understand more comprehensively, what large means here. Is it just bigger size, say XXL compared to M or S, or gypsy skirt compared to office style skirt (not sure exactly how it is called, maybe pencil skirt, is it?)