Luke is more powerful than Obi-Wan. Both Vader ("The Force is strong with this one" from Ep. IV) and Emperor ("The Force is strong with him. The son of Skywalker must not become a Jedi" from Ep. V; and "you must bring him before me. He has grown strong. Only together can we turn him to the Dark Side of the Force" from Ep. VI) acknowledge it.
In Legends canon, Luke explicitly is noted to have the same super-high Midichlorian count as Anakin, meaning he's stronger in the Force than Obi-Wan
Obi-Wan especially isn't good at "minding the Living Force", as Qui-Gon noted in Episode 1.
Luke has familial relationship with Vader, which probably helps attune their feelings and force connections to each other. Not 100% certain from canon, but can be inferred from, for example, Leia also sensing Luke's distress when saving him in Cloud City at the end of Episode V.
Similarly, Vader can sense Luke's presence even when the Emperor cannot in Episode VI:
Darth Vader: My son is with them.
The Emperor: Are you sure?
Darth Vader: I have felt him, my master.
The Emperor: Strange that I have not. I wonder if your feelings on this matter are clear, Lord Vader.
Luke is inherently compassionate in general (and this especially intertwines with Vader being his father) - which is in contrast with Jedi (like Obi-Wan) who are trained NOT to emotionally entangle themselves since a very young age:
Darth Vader: He will come to me?
The Emperor: I have foreseen it. His compassion for you will be his undoing. He will come to you and then you will bring him before me.
Darth Vader: As you wish.
Obi-Wan is prejudiced against Anakin - this was the man who was his friend and "The Chosen One", who betrayed both their friendship and entire Jedi Order and entire Republic - and murdered a Temple full of Jedi younglings. Luke didn't have that coloring his feelings. (H/t for @Thomas noted in the comments)
My first instinct would be to say that Darth Vader had compassion for Luke, because Luke was his son, and not for Obi Wan (who was his enemy), and so Luke was able to pick up on that. Also, Darth Vader may have been "softened" by Luke's attempts to reach out to him, and this may have made his feelings come more to the surface.
I also think #3 is a strong possibility. Luke had a connection with Laia because she was his sister (after Darth Vader cuts his hand off, he reaches out to her telepathically.)