I used RED so show the main differences between the two passages.
Psa 14:1 To the chief Musician, A Psalm of David. The fool hath said in his heart, There is no God. They are corrupt, they have done abominable works, there is none that doeth good.
Psa 53:1 To the chief Musician upon Mahalath, Maschil, A Psalm of David. The fool hath said in his heart, There is no God. Corrupt are they, and have done abominable iniquity: there is none that doeth good.
Psa 14:2 The LORD looked down from heaven upon the children of men, to see if there were any that did understand, and seek God.
Psa 53:2 God looked down from heaven upon the children of men, to see if there were any that did understand, that did seek God.
Psa 14:3 They are all gone aside, they are all together become filthy: there is none that doeth good, no, not one.
Psa 53:3 Every one of them is gone back: they are altogether become filthy; there is none that doeth good, no, not one.
Psa 14:4 Have all the workers of iniquity no knowledge? who eat up my people as they eat bread, and call not upon the LORD.
Psa 53:4 Have the workers of iniquity no knowledge? who eat up my people as they eat bread: they have not called upon God.
Psa 14:5 There were they in great fear: for God is in the generation of the righteous.
Psa 14:6 Ye have shamed the counsel of the poor, because the LORD is his refuge.
Psa 53:5 There were they in great fear, where no fear was: for God hath scattered the bones of him that encampeth against thee: thou hast put them to shame, because God hath despised them.
Psa 14:7 Oh that the salvation of Israel were come out of Zion! when the LORD bringeth back the captivity of his people, Jacob shall rejoice, and Israel shall be glad.
Psa 53:6 Oh that the salvation of Israel were come out of Zion! When God bringeth back the captivity of his people, Jacob shall rejoice, and Israel shall be glad.