It would outsell Switch for a few weeks until the Lite releases then get overtaken again. But at this point Sony is more concerned about profits rather than "winning" weekly sales against a device that is coexists very well with. Switch is not stealinf PS4 sales to any notable degree and vice versa.
I think Trump might be another reason as to why they are not cutting the price right now. I know I wouldn't when there's a possibility of 20% tariff being slapped on consoles sales, as that would make the console more expensive again for Sony, Nintendo and Microsoft.
The next round of tariffs has been delayed until after the holiday season to not hurt those sales, but then early next year they may very well come. And if it comes, it may also just as well increase the price of the next gen by 100$ in the US.
The Nintendo eShop rating Thread: http://gamrconnect.vgchartz.com/thread.php?id=237454