I know for many of you this is a big issue, which one to use? I have adopted the policy of using whichever I am dressed for, I work on the theory that this is less likely to embarrass the civilians.
That does mean that I am almost uniquely qualified to compare the two alternatives. We will all have noticed that very often the ladies are under catered for, hence the long queues we so often see outside the ladies' door, for those of you not familiar with the inside of a ladies' I can assure you that the queue continues on the inside. Often you will find that there will only be three or four stalls, while the men will have six urinals and one or two stalls, often only taking up roughly the same footprint on the ground. Another reason for the queues is the difference in the amount of time it takes a man to walk in "present arms" and walk out again, against a lady disrobing, adjusting her dress, washing hands, and a quick check in the mirror ~ note washing hands, it is a little frightening how few men I see washing their hands.
Final word on the subject, just around the corner from where I live is one of our area's few blue plaques, it marks the home of one of the most influential of Victorian innovators, Thomas Crapper. (Funny how Google speller doesn't like "ickier" but is fine with Crapper!)