It depends on the character. If it's relatively minor character like Mark or Jack, there's not much difference to the overall story. If it's a major character like Holly though, there's a greater degree of change, both to Lena and Holly's personalities.
The trajectory of the narrative for the most part stays the same. Some choices allow you to choose whether to go to certain events, although that seems to happen more on Ian's side. For example the choice of going to Cindy's birthday or going to a book fair with Holly. But there is some effect on Lena's side. For instance, she only travels abroad if she works with Seymour.
There are plenty of scenes that are tied to specific relationships, and where there are events that happen on every route, there's usually some kind of dialogue difference dependent on who is who at least.