A year ago Manchester City Women's Football Club were called Manchester City Ladies Football Club. Their rival teams tend to still have Ladies in their name: Chelsea Ladies, Arsenal Ladies, Liverpool Ladies and many more. In a piece on the Radio 4 Today programme this morning, Stephanie Houghton, Manchester City Women's FC captain talked about the rebranding exercise and said that the word women is more powerful than ladies and allows people to respect the team more (Listen here).
I agree with Stephanie. Lady is a very loaded word, even though some women like it, as they have been brought up to see it as a polite variant. Referring to women as women is certainly more powerful than using the word ladies. Low-status job titles often include lady eg dinner lady, cleaning lady, tea lady, lollipop lady (the opposite of which is lollipop man, not lollipop gentleman). You wouldn't talk about an artist having a one-lady show, or about a group calling itself 'Ladies for Equal Pay' or something similar. Men's organisations often have a ladies' offshoot, or have an annual Ladies' Dinner or Ladies' Night, but women's organisations formed in their own right usually term themselves women eg Townswomen's Guild, Women's Institute.