You can have both, Payton Manning, Tom Brady, Troy Aikman, Steve Young, Joe Montanna, and John Elway all had stats and Big Rings in the modern era.
In fact if you look at the history of the Super Bowl there are a lot more quarterbacks who have gaudy numbers winning, and participating in it than not.
I think Jakes stats are misleading. He makes big plays at the most critical of times. His coach does not want a passing offense and often Jake is in a bad down and yardage situation when asked to pass.