Either can work. It's all about balance (does something on the other spread counteract the white space?) and consistency (do you treat other story ends in the same way?).

yep, either is ok... or you might try a more organic layout, where the text follows a curve, so ends a bit higher on the first one, similar height on the second, and so on...

That rule at the bottom of the second page of the spread doesn't serve any useful design purpose. If it's to indicate the end of a chapter, that's already obvious from the fact that the text doesn't fill the page. It is especially unnecessary if you choose the column alignment where the left column goes to the bottom of the page. But unless you plan to have a rule at the bottom of all pages, I would eliminate it in either alignment scenario.

Thank you for the answers!

About that rule at the bottom: it is a footnote, this made me think about a second question. Do you think extending it under both columns is a good idea or should I leave it only under the column it is referencing? (in this case balancing columns would be silly imo)

I'd leave it under both.

If you're gonna rag the layout, you can use the "hang from the washing line" concept -- rag bottom, so that all elements snap to the w-line, but hang by varying amounts.

I tend to follow what Nick is suggesting. Or at least what I'm reading into it. I always protect against widows and orphans. It is, for me, more important that a thought begins and ends cohesively than the bottom of the page always align. I tend to like a little vertical rag, it helps add variety too.