Punting is less messy. You can keep it discrete and no bunny boiler is going to turn up at your door. Most of the times it just business and no broken hearts.
Affairs are a bit more passionate and exciting because the girl wants to fuck you and there are some feelings there. If you are in a relationship then you are playing with fire and also risk getting hurt yourself.
So though affairs have potential to hit higher highs, I don’t think they are worth the headfuck.