I can speak only for myself, a 30 year old woman.
For me "ladies" connotes a more delicate being than "woman"; one who is a bit precious, and needs some sort of shielding from the uglier parts of life. I think this connotation implies an inability to fully participate in seriously in the public sphere, which is often ... untidy i.e. positions of power requiring decision making in gritty circumstances and access to skills/information which belong to the realm of the less-than sanitized.

Although JP Sartre's play "Les Mains Sales" is more of a discussion regarding the ethics of effective political action, this quote applies quite nicely to my preference of the word "woman" to "lady". A character who is a political activist during WW II says:
"Moi j'ai les mains sales. Jusqu'aux coudes. Je les ai plongees dans la merde et dans le sang" (My hands are filthy. I've plunged them in blood and s**t up to the elbows).
Life is messy and not always sweet.I think a ladylike attitude is a barrier to fully participating in the public sphere. As a citizen, I have my sleeves rolled up.