Oak for me.

It depends what you are trying to achieve. As you say, they are two different looks.. one bring more understated and blending into the bank ground - matching with window cill.
What other furniture is in the room? Is their a bed/cot? Is it Oak?

White works beautifully with wood and would allow you to play with colour and texture more with whatever you style on the shelves.

White. Less cluttered and also highlights the lovely oak chest of drawers.

White it is, thank you everyone!

I’d paint it the same colour as the wall.