Depends on the type of website honestly. I imagine why things like this have been left up to developers. Live blogs will use pull down, and messaging web apps will use a pull up gesture.
I think a pull down approach works best with a native implementation, because it’s an expected behaviour across a lot of apps, and most websites, I think, will work better with pull down than swipe up. Only really discourse forums that I frequent where it wouldn’t work.
The ideal direction depends on where new content shows up. If it shows up at the top, like emails, live blogs, and news websites do, you pull down to refresh. If new content appears at the bottom, like on most forums and messaging sites, you’d want to pull up.