Given Barkov's offensive production as a PPG player over the past couple of seasons, coupled with his unquestionably elite defensive game (like, best in the league elite), two of three conditions would have to be required in order for someone to even think about taking Pettersson in this poll.
1). You would have to believe that Pettersson is going to be one of the top two or three most dominant offensive forces in this league for the forseeable future, enough to create a significant gap between himself and the level Barkov is currently occupying. Thinking along the lines of a consistent threat to go between 100-110 points in a season.
then:
2). You have to believe that Barkov won't improve signifcantly, if at all, on the offensive end over the coming years. This seems highly unlikely, given Barkov's age, and the fact that he hasn't had the best cast of linemates to this point either.
or
3.) You would have to belive that Pettersson will himself an elite defensive forward as well, maybe not on Barkov's level, but enough to mitigate the gap.
This is where it could get dicey - while his intelligence and stick work does some credence to the idea that he will be an excellent two-way threat down the line, Pettersson's frame and strength levels are so underdeveloped that it becomes damn near impossible to discern where he'll actually end up in this facet. It all depends on where he actually tops out physically, and more importantly, how he's able to use the newfound strength.
Odds aren't great, but it's totally possible that Pettersson ends up a better player than Barkov. If I was starting a franchise from scratch, I'd still probably take Barkov, given that his floor is a dominant two-way center that can anchor your first line for 10 years.
However, I could absolutely see someone taking Pettersson as a pure gamble on his offensive upside, which I do think surpasses Barkov's.