Contrary to popular belief they are not the same person.
The way she treats Ichigo is not the way she treated Kaien. Both gave her a sense of normality but in different ways.
With Kaien she was not Kuchiki, the ice princess. She was merely Rukia. He was her friend and for that she admired him. Yet at the same time, he was also her superior. She would never disrespect him in words or thoughts. She'd never dream of such a thing.
With Ichigo it was different. They were equals. She'd never called him Ichigo-dono and hell if she'd start now. She argued with him, called him names, but at the end of the day they understood each other.
There may have been a time when their physical similarities haunted her but simply get to know Ichigo and you'd realize how absurd it was to ever compare him to Kaien. Looks aside, they weren't remotely similar and she wouldn't have it any other way.