All Virgin is is a shell with name licensing and some style guidance - the 3 Virgin airlines are independent companies that have no relationship except the name.
Small sample set but The one time I travelled from Seattle to Sydney on Virgin Australia I could not get Virgin America to check the bags all the way through. Oddly on the way back, they were checked into my Alaska flight. I liked both Virgin Atlantic and Virgin America the couple of times I flew them but VA was always a load more expensive on the same routes.
In his PR tour for Virgin Atlantic opening up Seattle-LHR this week he spent an inordinate amount of time dissing Alaska Air.
/i