TL;DR: Either one is correct, but "They are us" is much more commonly used in everyday language.
There is something called a "predicate nominative," which is "the adjective (or adjective phrase) or noun (or noun phrase) that follows a linking verb to complete its meaning" (Merriam-Webster), and it should take the subject form, ie "we" instead of "us", or "I" instead of "me". This has long been considered "technically correct", and generations of grammar teachers have insisted that it be used.
However, in everyday language, most people use the object form in these cases. Even though some grammar teachers may not like it, the object form is correct as well, although less formal in style, and most importantly, the majority of people consider it the "normal" way of speaking. You can use either one, but the "us" form here is common in most usage, and the "we" form can sound overly formal.