Se as consultas existentes fazem o que você quer/precisa,
UNION tornará muito simples combiná-los, algo como; SELECT * FROM (
SELECT is_private 0, <field1>,<field2>,<field3>, ... ,(SELECT COUNT(*)
FROM votes
WHERE message_id = m.message_id
AND vote_type = 'like') AS likes,
(SELECT COUNT(*)
FROM votes
WHERE message_id = m.message_id
AND vote_type = 'dislike') AS dislikes
FROM messages m
WHERE 1 #and hidden is null
and recipient_id = 1
UNION ALL
SELECT 1, <field1>, <field2>, <field3>, ... ,(SELECT COUNT(*)
FROM votes
WHERE message_id = m.message_id
AND vote_type = 'like') AS likes,
(SELECT COUNT(*)
FROM votes
WHERE message_id = m.message_id
AND vote_type = 'dislike') AS dislikes
FROM private_messages m
WHERE 1 #and hidden is null
and recipient_id = 1
)
ORDER BY datetime DESC
Observe que você precisa selecionar o mesmo número/ordem de colunas de ambas as consultas para que a união funcione.
SELECT * torna difícil verificar se/que esse é o caso. Se 
