I wouldn't say exclusively that one factor carries more weight than the other, I'd say it's a balanced combination of the two.
As far as stats are concerned, goals and assists are the two main ones but there are other very telling stats like dribbles completed, passes completed, pass accuracy, goal scoring rate, etc. that can provide an accurate depiction of player productivity. What other measurements would you consider to determine player of the year award? If they are things like dribbling, accuracy, goals scored in Finals, game winning goals/assists etc, those can all be determined as statistics too. Something to consider when downplaying the value of a well rounded stat sheet.