I've done all 6 Origins, always as a female character. I felt the most emotional pull with my City Elf Warrior, seconded by my Human Noble Warrior. Both women had compelling, very emotional stories. I felt as if I truly understood their motivations, their vulnerabilities and their bewilderment in how their stories unfolded. Both were adrenaline-filled openings. By the time those openings were done, I was determined to see these women succeed.
I finished the game with the Human and am currently working on finishing with the City Elf.
As far as my least connected, it's a tossup between my Dalish rogue and my Human Mage. They just weren't as compelling as the City Elf and Human Noble. I wasn't moved at all by their plights.
My Dwarven Commoner Rogue earned more sympathy from me than did my Dwarven Noble Warrior but still, I wasn't totally invested in either of their stories.
I wonder if I'd feel differently about the openings had I played male characters?
As a side note, I like how the game integrates all the beginning stories into the overall plot. It's a nice touch to see someone who played a big part in my Human Noble's origin show up further down the road in my City Elf's experience. Ties them all together and, for me, helps to make it feel more like a real world with real, intersecting stories.