They were the same but not, that was the least confusing way to describe themselves. Them. Singular? Well, he tried not to think about it. He had insisted that he was the same man, and in many ways he was. The Doctor now had carried on in his predecessor's vision, the last sight for those eyes being her and the same of him. She mellowed him out, balanced him. Rose gave him a semblance of peace he thought lost after the Time War.
He didn't want to lose her, so he'd done everything he could to keep her by his side while he discovered just what sort of man he'd become with this face.
The Doctor nodded faintly as she spoke, his eyes and ears focused solely on her. "I was the same person," he eventually volunteered once she'd said her piece in its entirety. "But, you're right, Rose. I grew, I changed. It isn't just memories that make us the people we know, it's the way we're seen. Perceived. Fancied. Abhorred. Adored. Feared. Loved. All of those things make me different from every other me that came before and the ones yet to come. It's my name, the things that I've done, the things I'll always do, that make me the Doctor."
Scooting that much closer to her, the Doctor mirrored her gesture by palming her cheek. Forehead to forehead, he plunged forward with sentimentality as his only defense. He didn't feel like he'd hurt her, but he had neglected to reassure her. That was new territory to him, of course. But it was good, it was fun. She taught him something different everyday about people.
One of the many things he loved about Rose Tyler.
"And, it's the way you see me that makes me me, Rose Tyler."