Without seeing the space, I think either one would work. Black on the stairs will show scuffs and scratches more, as well as dust.

"Modern farmhouse style" is rather ambiguous.

Staircase design may come into play, but really comes down to your preference.

We are matching ours. We paid extra for this when we ordered the flooring.

You can go in several ways. There is no firm rule just make it as aesthetically pleasing as possible. If the home is a vintage home, keep consistent with vintage of home. Some photos would help me give more specific advice.

I love those black steps with the light floors, but it it’s true, you’ll have to look at scuffs and dust unless you have a live in maid

We had a new oak staircase installed a few years ago. Our fabulous carpenter, who specializes in staircases, spent a lot of time matching our staircase stain to our porcelain woodlook tile flooring. We love his workmanship!! I think there is no right or wrong in matching or not matching a staircase to flooring. It is all about your personal style!

I prefer matching.

Non-matching has to be done well, so that it doesn't look like the house was patched together without a unifying design theme.

Good question. Based on what I've seen in my life I'd say no. But to be sure I looked a countless pictures of staircases which confirmed my opinion. Some do match the treads with the floor but few matched the treads and the riser boards.

I noticed those matching the floor color completely did not look good with a washed out look, but those with different colors helped the staircase stand out and many looked great. Saw some black treads offset with different color riser boards and didn't look to bad, but not something I'd do. The worst was black on black to any floor color. I prefer carpet on staircases and don't like the constant clunk, clunk, clunk with every foot step. Babies can slide down the stairs easier too.

Do the stairs lead to a window, or just another level in the house?

It's never wrong to have all wood flooring to match throughout, including stair treads. It might not always be necessary, but it's never wrong.

Stairs should definitely match the floors.

I dislike the pictures above with black stairs.

Looking at our stair "inspirations" for current build--all from AD etc--I see that wood matching wood is the rule; and if the flooring is not wood, it still matches.

arch., John Bornas

But, not to be judgemental, opinionated and biased, it's your house, your choice.

My concern with matching would be that if it matches too well, it can be hard to see the bottom step vs. the floor. (Source: my mom broke her leg by missing a step because the bottom step matched the floor so well.) Some folks (elderly, very young, someone not wearing their glasses...) might benefit from a visual cue for the last step, even if it's just a thin part like the nosing stained a bit darker than the tread and floor.

Consider sturdy handrails going the entire length of the stairs, extra lighting and (perhaps) contrasting riser and stair colours. There are different considerations if this is an elder-care home or publicly accessed building.