The most striking similarity in these two scenes is the realization of Hamlet (1.2), Marcellus and Horatio (1.4) that things are not right in Denmark and the state of the monarchy.
Hamlet has the more complete thought process in his soliloquy (1.1.133-165). Here, he is mourning the loss of his father, ("So excellent a king") the treachery of his mother ("frailty, thy name is woman!"), and the unfitness of his uncle to be king ("My father's brother, but no more like my father/Than I to Hercules.")
Marcellus has the same sentiment but expresses it much more succienctly: "Something is rotten in the state of Denmark" (1.4.100)