Question about moving my cats to a new place / separation anxiety?

I would definitely take both of them. While it is very true that cats are more attached to heir places than their people, if they are attached to other cats, that is important too. It will make the move much easier for both of them if they go together. If they are scared, they will have each other to reure them. It shouldn't take them more than 3-5 days to settle in if they are together, however, if you take only one, it could take months.