Combine três consultas SQL

Isso pode funcionar para você.

SElECT COUNT(*) AS imgCount FROM (
    SELECT imgHeight, imgWidth, imgId AS primaryId FROM primary_images
    UNION ALL 
    SELECT imgHeight, imgWidth, primaryId FROM secondary_images
) AS union_table
WHERE primaryId = $imgId 
AND (imgWidth != $maxImageWidth AND imgHeight = $maxImageHeight
OR imgWidth = $maxImageWidth AND imgHeight != $maxImageHeight
OR imgWidth = $maxImageWidth AND imgHeight = $maxImageHeight);

Também acredito que isso seja equivalente, embora não tenha certeza.

SElECT COUNT(*) AS imgCount FROM (
    SELECT imgHeight, imgWidth, imgId AS primaryId FROM primary_images
    UNION ALL 
    SELECT imgHeight, imgWidth, primaryId FROM secondary_images
) AS union_table
WHERE primaryId = $imgId 
AND (imgWidth = $maxImageWidth OR imgHeight = $maxImageHeight);

De acordo com a solicitação, aqui está uma única consulta que retorna 3 linhas.

SELECT 'ALL EQUAL' AS COL1,COUNT(*) AS imgCount FROM (
    SELECT imgHeight, imgWidth, imgId AS primaryId FROM primary_images
    UNION ALL 
    SELECT imgHeight, imgWidth, primaryId FROM secondary_images
) AS union_table
WHERE primaryId = $imgId AND imgWidth = $maxImageWidth AND imgHeight = $maxImageHeight
UNION ALL
SELECT 'WIDTH EQUAL' AS COL1,COUNT(*) AS imgCount FROM (
    SELECT imgHeight, imgWidth, imgId AS primaryId FROM primary_images
    UNION ALL 
    SELECT imgHeight, imgWidth, primaryId FROM secondary_images
) AS union_table
WHERE primaryId = $imgId AND imgWidth = $maxImageWidth AND imgHeight != $maxImageHeight;
UNION ALL
SELECT 'HEIGHT EQUAL' AS COL1,COUNT(*) AS imgCount FROM (
    SELECT imgHeight, imgWidth, imgId AS primaryId FROM primary_images  
    UNION ALL 
    SELECT imgHeight, imgWidth, primaryId FROM secondary_images
) AS union_table
WHERE primaryId = $imgId AND imgWidth != $maxImageWidth AND imgHeight = $maxImageHeight;