What does Buddhism say about polyamory?
Buddhism is not conserned with the title of the romantic relationship or the sexual orientation of the partners in it.
Buddhism goes much deeper than that, it looks instead at the defilements that are connected with romantic relationships, e.g. "lust, craving, desire, jealousy, hatred etc."
Is it any different than a romantic relationship between two people?
It is not. The above mentioned defilements, are the same no matter what kind of romantic relationship we are talking about.
Is it wholesome, unwholesome or neutral?
According to the Abhidhamma, there are 52 mental factors (cetasikas). 14 of these are unwholesome mental factors, among those are "hatred, jealousy, avarice, craving". They are of course also part of the 3 root defilements, i.e. greed, hatred and delusion.
If one or more of these mental factors are present, it becomes unwholesome.
Do different branches or traditions have different views on this subject?
Good question. I do not have an answer to that. I would think that it's the same opinion, since we are dealing with the root defilements. I might be wrong about this though.