Stefan/Katherine - "I love you, Stefan. We will be together again, I promise."
Okay, first thing first. I do not believe that Stefan is a boring character, or lacks any sort of personality. I believe that he’s interesting, he has a complex past (if you’ve been immortal for 145 years that’s sort of expected), and he has a great personality.
I believe though, that we see a different side of Stefan when he’s with Katherine instead of Elena. With Elena, he’s become this good-guy saviour, who is never going to hurt her. When he’s Katherine, his vampiric nature comes to the surface. He’s not so much the good guy anymore. In my opinion, he becomes more real.
“You haven’t changed at all, have you?” - Stefan Salvatore “But you have. You’re stronger, meaner. Sexy.” - Katherine Pierce
Katherine has spent the last 534 years surviving as a vampire, running from Klaus and the Originals (If that’s the theory we’re working under). She’s been living under the mental capacity of kill or be killed, doing whatever she could to survive.
When she’s with Stefan, you see her humanity. She can be fun and playful and human around him. Whether or not she should, she feels like she can let her guard down.
She could have continued on, ignoring that Stefan was out there; but she continued to track him down over the years, checking in on him.
You were watching Bon Jovi, and I was watching you - Katherine Pierce
Stefan is not, nor ever has been, indifferent to Katherine; that’s evident in just how easy it is for him to get worked up around her, how easy it is for her to get a reaction out of him, in nearly anything she says.
He’s had so many chances now to kill her, but he can’t do it. He’s hesitated nearly every time.
This is the only place that has remained constant. This room holds every memory that I ever thought was important enough to hold on to. - Stefan Salvatore
He held on to Katherine’s photo for nearly a century and a half. It remained secure in the room where he held every memory that he thought was important enough.
As far as we know, that photo is still in his bedroom. It was definitely there when Katherine appeared at the house.
He might have buried his feelings in his conscience, but in his subconscious everything he felt was still there. He just never dealt with it, deciding that he hated Katherine. He decided that the love he felt with Katherine was only her compulsion; when she never actually compelled his love, but instead compelled away the fear he felt when he found out exactly what she was.