Niet alles is een unie -- in dit geval is het een join op de subquery's:
SELECT shpUserAdded AS userName, merCount, prdCount
FROM (SELECT shpUserAdded, count(*) AS shpCount FROM shops GROUP BY shpUserAdded ASC) AS s
JOIN (SELECT prdUserAdded, count(*) AS prdCount FROM products GROUP BY prdUserAdded ASC) AS p
ON (shpUserAdded = prdUserAdded);