Both stories speak of a wicked man who wanted to destroy God's people:

"Laban... sent his servants to slay us..." (1 Nephi 3:25)

"The next day Holofernes commanded all his army... to make war against the children of Israel." (Judith 7:1)

Both claimed that God's strength did not depend upon numbers:

"the Lord... is mightier than all the earth, then why not mightier than Laban and his fifty." (1 Nephi 4:1)

"For thy power standeth not in multitude, nor thy might in strong men... a saviour of them that are without hope." (Judith 9:11)

In both cases the wicked man was delivered into the hands of the servant of the Lord:

"I beheld a man, and he had fallen to the earth before me…" (1 Nephi 4:7)

"And Judith was left alone in the tent, and Holofernes lying along upon his bed…" (Judith 13:2)

In both cases the wicked man was drunk.

"he was drunken with wine…" (1 Nephi 4:7)

"he was filled with wine…" (Judith 13:2)

In both cases the servant of the Lord took hold of the wicked man's weapon:

"I beheld his sword, and I drew it forth…" (1 Nephi 4:9)

"she... took down his fauchion from thence…" (Judith 13:6)

In both cases the servant of the Lord took hold of the wicked man's hair:

"took Laban by the hair of the head…" (1 Nephi 4:18)

"took hold of the hair of his head…" (Judith 13:7)

In both cases the wicked man's head was cut off with his own weapon:

"and I smote off his head with his own sword…" (1 Nephi 4:18)

"And she smote twice upon his neck... and she took away his head from him." (Judith 13:8)

In both accounts the servant of the Lord changes apparel:

"I took the garments of Laban and put them upon mine own body; yea, even every whit" (1 Nephi 4:20)

"She... pulled off the sackcloth which she had on, and put off the garments of her widowhood... her countenance was altered, and her apparel was changed" (Judith 10:2-3, 7)