The difference between Chow down and Eat up

When used as verbs, chow down means to eat, especially to eat vigorously, whereas eat up means to consume completely.

check bellow for the other definitions of Chow down and Eat up

Chow down as a verb (idiomatic):

To eat, especially to eat vigorously.

Examples:

"We're all famished; it's time to chow down."

Eat up as a verb (ambitransitive):

To consume completely.

Examples:

"He was so hungry that he ate up everything on his plate."

"Dinner is served. Eat up!"
Eat up as a verb (transitive, figurative):

To cover (a distance or an amount).

Examples:

"His behavior has eaten up all the goodwill we felt towards him."
Eat up as a verb (transitive, figurative, informal):

To accept or believe entirely, immediately, and without questioning.

Examples:

"She ate up everything that her image consultant said."