On the surface it seems like you need a doubling of power, but it's also a question of what needs to double. The GPU needs to double how often it rasterizes the layers. But for the most part, everything on screen should already be available to the GPU, and doesn't incur a CPU hit. What does incur the CPU hit is drawing new content that isn't already in layers.
Scrolling is a good example of both. Scroll a little bit, and the odds are good that the CPU has already drawn all the content, so the scroll is just leaning on the GPU to redraw the existing layers in new places. Scroll a lot, and then the CPU has to work to fill in the gaps where content wasn't yet drawn. This is when scrolling stops being smooth, if too much work has to be done.
But also, if you are scrolling, you don't pay much of a CPU penalty for going to 120Hz from 60Hz. There's a bit of work the CPU does by doubling how many refreshes it does per second, but you don't really draw new content any more frequently. If the scroll is 500 pixels per second, for example, that is what tells me how much drawing I need to do. Even if you double the refresh, you are still scrolling at 500 pixels per second, and done correctly, you can break down the work that would have been done in a single refresh at 60Hz across two 120Hz refreshes to keep it smooth.
But the general rule here I think is this: If something wasn't smooth before, this won't make it any better. If it was smooth before, it has the chance to get even better. I suspect we will see a lot of apps floating between 60 and 120Hz for a while on the new hardware, that were handling 60Hz nicely now.