No. Bitcoin is not silently losing against privacy coins but it will go reverse instead and I don't think there is war against each other because they are far from competetion. In my own opinion privacy coins are only capable of dominating online transactions and governments will surely prohibit the use and trade of such privacy coins unlike Bitcoins that is accepted in some countries and central banks so I think that is one of the advantage of Bitcoin in terms of adoption and usage. The governments will think that those privacy coins are made to be used for criminalities and any illegal activities because it has tighter and untraceable technology.