I know that this was partially answered here but I seem to have found a contradiction between page 82 and page 282 of the core rules. In brief, page 82 says that if both characters succeed and neither side scores more momentum than the other, then the active character i.e. the attacker succeeds. While page 282 by contrast suggests that there could be a draw which can get resolved by momentum (or threat) spend. I realize that the two aren’t necessarily contradictory; it would mean that in a tie if neither side spends additional momentum/threat that the attacker wins, but if either side chooses to spend, that whoever spends more wins. However, normally a PC can only spend momentum to increase their # of successes before the dice are rolled (Create Opportunity, page 85) and you will only know if there’s going to be a tie after the dice are rolled. A PC could opt to Succeed at Cost as suggested on p282, but why would they, if they’ve already tied and they are the active character?
I actually do not read that on p. 282.
I would interpret this as to mean that a Player character can succeed (at cost) over an active NPC. Maybe by GM’s discretion.
The text is indeed very open to interpretation.