It would be cool if there were some gender specific quest options such as you need to sneak into the chantry and male characters have to sneak through the back, but females have the option of posing as a priest (or either gender could pass the equivalent of a speech check and convince the priests they are making a delivery or something) or a much less savory example would be something like a female rape victim only being willing to open up to a female PC. Your female PC could express fear of becoming a broodmother when in the deep roads, talk about pretty pretty dresses with other female NPCs/companions, etc...
Actually in Origins, even men can get in on the 'pretty pretty dresses' conversation - a mage Warden of either sex and Alistair can start off talking about why Alistair is a templar and get sidetracked onto which side has a more fashionable uniform. Which, I might point out, involves floor-length skirts on both men and women. Now there's a side to the Mage-Templar debate you don't see often. Also, both men and women can talk with Leliana about shoes, though the hair conversation is restricted to women. Besides, we're going to Orlais, with Vivienne. Everyone should have the chance to gossip about the newest trends in court fashion.
Dialogue like with the guards in the CE origin quest, who will make a whole bunch of race and gender-specific offensive comments while you smile and serve them poisoned brandy. (The option to murderknife them in the eye instead should remain).
A woman having difficulties with Qunari diplomacy, because they're too busy trying to wrap their heads around the blatant gender role violation to talk about trade routes.
A man having equal but different difficulties with Qunari diplomacy, where they take him back to their leader and she takes a very dim view of negotiating trade with a man.
Two women in the aftermath of a broodmother fight having a shaken conversation, promising that they'll kill each other before they let the darkspawn take them.
A chevalier not wanting to duel a woman to the point of calling the whole thing off - at least unless you throw down the gauntlet yourself because you WANT to fight and he's not weaseling out of it that easily.