The latter is easier on your joints, especially your knees. Also, you are less prone to "cheat" with inward rotation if you open from seated, particularly if you rotate outward first. For box splits, descending from standing is easier, but again it's tough on the joints, knees especially. I recommend going into box splits from the frog stretch, although IMO box splits don't provide anything that a good side split gives you (unless you are overly flexible).
Bottom line: from sitting is best IMO. Others may have different opinions based on their experience.