as children or like children

Both sentences are grammatically correct, though as is more preferable.

According to Merriam-Webster's Dictionary:

'There is no doubt that, after 600 years of use, conjunctive like is firmly established. It has been used by many prestigious literary figures of the past, though perhaps not in their most elevated works; in modern use it may be found in literature, journalism, and scholarly writing. While the present objection to it is perhaps more heated than rational, someone writing in a formal prose style may well prefer to use as, as if, such as, or an entirely different construction instead.'