The advantages of UA over BA are free seat selection, much better IFE, incomparably better App and website for managing your booking and it uses T2 which is a far nicer terminal T LHR. Also UA has a significantly better on time record.

The advantages of BA over UA are friendlier FAs, better food, a lighter cabin (UA goes out of its way to get people to close their window shades even in the middle of the day) and arrival at JFK which is better for more (but not all) parts of NYC. Also you get Avios which may be important.

Can’t speak to VS.

So you takes your choice. As a UA elite entitled to Economy Plus I would not even consider BA.