While "open up to someone" and "warm up to someone" are similar in meaning and often used interchangeably in informal conversation, they do have subtle differences in connotation.
"Open up to someone" generally refers to someone becoming more emotionally or personally honest and revealing their thoughts, feelings, or inner struggles to another person. It implies a deeper level of trust and vulnerability in the relationship. For example:
"After months of dating, she finally opened up to him about her childhood trauma."
"Warm up to someone," on the other hand, indicates someone becoming friendlier, more receptive, or more comfortable with another person over time. It doesn't necessarily involve sharing deep emotions or personal experiences, but rather a shift from initial reserve or hesitancy to a more positive and welcoming attitude. For example:
"At first, the new employee was reserved, but she has warmed up to her colleagues and is now more sociable."
In the context of your sentences:
"It seems that he finally has opened up to you." suggests that the person has started sharing more personal information or feelings with the other person, indicating a deeper emotional connection.
"It seems that he finally has warmed up to you." suggests that the person has become friendlier or more receptive to the other person, possibly indicating that their relationship has improved or become more comfortable.
In many cases, these phrases can be used interchangeably without drastically altering the overall meaning of the sentence, especially in casual conversations. However, if you want to emphasize the level of emotional disclosure, "open up to someone" is more appropriate, and if you want to emphasize the improvement in the relationship's dynamics, "warm up to someone" fits better.