... and that's silly, because centers collect more points due to their position on the ice.
If offensive production is similar, the winger is better - at least offensively.
That is not how it works. There are many players who have switched from center to wing and vice versa over their careers, and there is no statistical proof that players would produce more as centers. In fact some players see their production dip while playing center, because they focus more on center's defensive duties and can't cherry pick or cheat as much. It depends on the player of course.
It is true that centers collect easy extra points from for example just winning offensive zone face offs, but they also lose potential points for having more defensive duties.