As other answers have stated, both phrases convey the minimal information "We are not natural citizens of this place." If that is all you intend to convey in a casual exchange, the phrases are equivalent.
However, there are additional weak implications that accompany each phrase. They are unlikely to be noticed in casual conversations, especially if english is not a native language, but could have meaning in a setting where people are expected to choose their language carefully, such as a legal proceeding.
"We are foreign." implies we are foreign to 'you', according to your rules. It applies to the group as a single whole. One person speaking for the group can truthfully declare that everyone in the group is foreign as long as he believes that fact to be true, regardless of his knowledge that one or more members of the group may not consider herself a foreigner.
"We are foreigners." implies that each of us consider our self to be a foreigner, by whatever standard each of us choose to use. The truthful speaker must believe that every person in the group individually consider themselves foreigners.
Credit to Baldrickk for initially calling out the difference in a comment.
Neither phrase implies that members of the group are from the same origin. Other suitable candidates do convey this, "We are French."
Therefore, by choosing these general phrases over the more specific; both topic phrases weakly imply that members of the group may be from different origins.