up to their necks vs neck-deep

up to their necks and neck-deep both are adjectives.

Word	Noun	Adjective	Verb	Adverb
up to their necks	No	Yes	No	No
neck-deep	No	Yes	No	No

As adjectives, up to their necks and neck-deep are synonyms defined as:

Other synonyms of up to their necks include up to her neck, up to his neck, up to my neck, up to our necks, up to your neck.

up to their necks (adjective)	neck-deep (adjective)
deeply involved	deeply involved