I thinkkkk it depends Like for Harry, and potentially Dumbledore *eyes the other discussion* the choice had an impact but it's also probably really to do for the sake of Harry at least, where the hat was able to see the horcrux and bit of Tom Riddle's soul which likely helped to contribute to the fact that Slytherin would help him on the way to greatness.

So the hat knew that there was a piece of soul in Harry that wasn't his, which I think made it weigh more heavily on the fact that he didn't want to be Slytherin and that hat could see it was Harry genuinely asking this.

Whereas Harry's middle child or Neville, there wasn't a genuine reason behind the choice. Neville was intimidated by Gryffindor's reputation, but as Dumbledore said at the end of year one about standing up for one's friends ... this was what the hat saw in Neville. Potential.