The divergences between Milton and Johnson are well documented. Johnson, who extensively wrote on Milton, is often described as an antagonist to the author of Paradise Lost. He certainly disapproved of Milton's anti-monarchist stance which had led the poet to justify the execution of Charles I and to become directly involved with the Protectorate of Oliver Cromwell. In his writings on Milton, Johnson challenged the poet's perceived political idealism, highlighting his quest for status and financial security. Writing at the end of the 1770s, Johnson particularly feared the appropriation of Milton's writing for revolutionaly purposes and sought to revise Milton's image as chamption of civil liberties.
A well-reserched and interesting book on the topic is Johnson's Milton by Christine Rees, Cambridge University Press, 2010.
According to Walter Jackson Bate, author of Samuel Johnson, Johnson, an Anglican, disliked Milton's Puritanism. Bate writes that Johnson included in his Life of Milton "a vein of antagonism... to Milton the man as there is to Puritanism in general" (Bate, page 537). Johnson believed that Puritans like Milton were rigid and, in Bate's words, capable of "self-deception" (Bate, page 537). Johnson found Puritanism too moralistic and inflexible.
In addition, Johnson disliked Milton's political ideas, which he referred to as "surly republicanism." Johnson was a Tory, which was the more conservative political party in England at the time (though he abhorred slavery and was in some ways liberal). In contrast, Milton was a civil servant under Oliver Cromwell, who was the Lord Protector of the Commonwealth of England after King Charles I was executed. Johnson took issue with Milton's tendency to "level down" rather than to "level up," meaning that Johnson felt that Milton brought the elites down to the level of lower classes rather than bringing the lower classes up to the level of their social betters. Johnson believed in an hierarchical society and disliked Milton's tendencies towards "leveling," or erasing societal distinctions.