Bigger screen means more power needed to light it up, but more pixels takes more computation to push the data. It probably varies how much of a factor each component is, but it's definitely both.

For two displays of different size with equal brightness showing the same image, the larger one will consume more power (at the very least (100% efficiency), the display will consume the amount of energy contained in the photons that are radiated out from each pixel).

But a larger screen won't necessarily require much more computation. Imagine showing photos, for example. The increased size of the memory copy (from disk to RAM to GPU), won't consume much more power, I would think.

And if it does, it will only be when loading the image to show it on the screen. After this is over, it will sit idle until loading the next image (consuming no additional power from use of CPU/GPU/storage).

For games, though, you're right. A higher resolution display will make a larger difference in CPU/GPU/storage power use, especially if the CPU is used, since the GPU is probably designed for a higher resolution display.