Both are nice, although the wood plank would probably be better if you plan to live in this place for a while. It could be refinished once the "boys" get bigger. Not so much on Engineered wood. Hard to say what would be best in your space without some photos? I think either one would look good, but best with kind of minimalistic look or Scandinavian look. What do you have now?

those look much more white?? Do these match the stairs? Kind of need more info here. This is picture with rug on old floor that has been removed?

this flooring looks amazing. Why are you removing it? I'm confused.

You don't need lighter for Scandinavian look. You just want blue/grays in furniture pieces and clean, minimal lines.

It is a great place and at least I know understand why you are doing the replacement. I think any of those choices work, just how you want to spend your money. Hardwood is expensive, engineered wood costs less. Generally speaking. I see a peak of stairs and none of those colors will go with the stairs. I wouldn't worry about the stairs. Just let them be. That is a huge, expensive undertaking.

Are you sure you can find a creative way to "fill the gaps" or whatever instead of replacing all that flooring? I think the stairs can "stand alone" without a big problem. We can decorate a bit to distract the eye and in a couple of days, you won't even notice that little issue. I love your place. The way the artwork is hung isn't the best, as usual, too high, but let's deal with the flooring first. I think I would go with the lightest color. Why? Because then it won't look like you "tried to match" but missed. So just make it totally different. That will work the best. Then, we can tie the stairs in by putting a wooden vase in that space near the stairs the color of the stairs and we can just make it all look cohesive.