Do women urinate more frequently than men if they drink same amount of water?

Depends on the individual, and the state of the individual's anatomy. Male and female bladders are about the same size and same volume, but because women have to make room behind the bladder for the vagina and uterus, the bladder often ends up wrapped in a sort of U over the top of the pubic bone. Men don't have to fit in those extra organs, so their bladder sits further back and less folded. Some women still don't have any problem "holding it" compared to men, but in general that fold over the pubic bone provides enough pressure on the bladder that women often do need to urinate more frequently.

I don't know for sure, but I've noticed that the women's restroom in a public place has lines of people waiting to go far more often than the men's restroom does.

A study was made and published many years ago at Stanford University, which compared thirty men and thirty women of comparative ages. Each of the men and women were paired by age group, then weight, metabolism, and several other factors in an attempt to match them as closely as possible. Each set of men and women were given equal amounts of water in large amounts. From what I remember, in almost all thirty of the paired studies, the women were able to produce a much larger quantity of urine in a 24-hour period than the men. I don't believe the study was concerned with the frequency of urination, but it was measuring input of liquid vs. output of liquid on men vs. women. I was invloved only to the extent of setting up and operating some of the lab measurements.

Capacity aside.

It seems to me that men usually urinate more often. But women hold it until its more of an emergency.

I'm not sure is this is a real psychological difference - or if it is just that much more impractical for women.

Seems like men are more likely to take an opportunity to go, even if they do not have too. Women won't usually actually go until desperate, even if given the opportunity. They will enter the restroom with friends but not go to the bathroom. Then they will need to stop on the way.

Yes, they do. A woman's bladder is smaller than a man's bladder, so it holds less fluid before it feels full.

Okay, I stand corrected - I was just sharing what I had been told and had read over the years.