Is what the article is essentially saying is that [1] is faster than [2]?

I have used [1] many times for that reason although [2] is probably more intuitive for what you want to do.

[1]

  SELECT vegetable_id, SUM(price) as price, SUM(weight) as weight
  FROM
  (
    SELECT vegetable_id, price, NULL as weight
    FROM prices
    UNION ALL
    SELECT vegetable_id, NULL as price, weight
    FROM weights
  )
  GROUP BY vegetable_id

[2]

  SELECT vegetable_id, price, weight
  FROM prices 
    JOIN weights 
      ON price.vegetable_id = weights.vegetable_id