Put the potatoes and sweet potatoes in a large saucepan and cover with cold water by 1 inch. Add a generous pinch of salt, bring to a simmer and cook until the potatoes are easily pierced with a knife, 35 to 40 minutes. Drain and let cool slightly. Peel the Yukon gold potatoes and transfer to a medium bowl. Peel the sweet potatoes and transfer to a separate bowl.
Divide the butter between the 2 bowls. Add the heavy cream and sour cream to the Yukon gold potatoes and mash well with a potato masher; season with salt and black pepper. Add the brown sugar and cayenne to the bowl with the sweet potatoes and mash well; season with salt and black pepper.
Dollop the potatoes and sweet potatoes into a warmed serving dish and swirl using a large spoon. (The potatoes can be made up to 2 hours ahead; set aside in a baking dish. Reheat, covered, at 350 degrees F, 15 to 20 minutes.)