Things will get worse for XB1, not better. Once both systems have a flood of games, 80%+ of which will be on both systems, it will be hard to justify buying the XB1 if the vast majority of multiplats look and play worse on the XB1. That leaves the XB1 to hardcore XB fans and people who can't live without the exclusives there.
The US should end with something like 50m PS4, 32M XB1, before next-gen starts opening up. Both the PS4 and XB1 had the unfortunate timing to launch with hardware specced around ~1080p on 28nm process tech, when we're about to hit 14nm/10nm and 4K adoption over the next few years. In that way, it reminds me of the pre-HD consoles launching vs. the PS2 (GC/XB).
It's not that the XB1 will be a failure in the US, it should certainly pull a profit. It's just that a weaker system with this rough of a start doesn't have the ability to 'dominate' anything. I'll be impressed if they pull 1:1 this year vs. the PS4 in the US in total hardware sales. They should definitely be able to win some weeks here and there, but they have a long hard slog until the price drops hit, and from there things should improve a bit.
People seem to forget about market and social intertia, and the lack of a significant head start and price advantage aren't on the XB side this gen. The rest of the world being dominantly PS this time around aside from possibly the UK is also a rough sign for them.
If anything, XB fans should rejoice that despite some solid hardware weaknesses, that the console should remain competitive and relevant in the US for years to come. But 'dominate'? Lol. No. Maybe next gen.