Whilst it can be somewhat subjective, and different styles of photography will benefit different amounts from exotic gear, it's surprisingly complex even in fairly narrow domains.

You're probably right that the first image wouldn't be significantly different on any other lens: it looks to be shot with a fairly narrow aperture in fairly unchallenging lighting conditions, so you're not hitting any of the aspects of photography where lens design has really advanced. A really cheap lens might show distortion or chromatic aberration (admittedly less important in B&W) at the edges, but beyond that, you'd be fine.

But I saw this article recently, and it's a sample size of 1, but nonetheless I found it somewhat surprising: https://petapixel.com/2018/08/15/is-the-sensor-or-the-lens-t... -- unfortunately it doesn't specify how these images were processed so it's hard to draw conclusions (eg: if it was all SOOC JPEGs, I'd be willing to believe that the older image processor in the D610 has worse highlight reconstruction, for instance. Or possibly worse demoasaicing). However prior to reading that article I'd have unconditionally recommended investing in glass before getting a new body; evidently my mental model for this was at least slightly deficient.

FWIW, my 2c: take photos that leverage the gear you've got, and conversely choose gear to get the kinds of images you want. Eg: I love my Nikkor 85/1.4G lens, despite its shortcomings, and you'll never get the same results on a smartphone (I mean, 85/1.4 is a pretty razor thin depth of field). If what you want is a super creamy background and tons of detail on the in focus regions, and you like the framing at 85mm, then that's pretty much the only way to get it (that I know of anyway). However, if you're only shooting wide angle, with everything in focus, then the differences will definitely be more subtle. They'll be there (eg: a Zeiss 21/2.8 on a D850 will pull out detail that the smartphone just won't know is there, the D850 sensor will have a lot more dynamic range, etc), but those differences will be less readily apparent, especially if you're viewing these images on a smartphone screen.

One last point: you're no doubt aware, but there are more dimensions to a lens' quality than its resistance to chromatic aberration (re: fancy APO optics), speed, or resolving power. I have a couple of the Voigtlander lenses for Micro 4/3, and while they have a lot of shortcomings, (so much coma aberration!), the way they render the background has a particular quality to it that's hard to replicate; not always desirable either, but sometimes fun. I also enjoy playing with some of the shortcomings: it will render with a kind of a halo-like glow around close objects when shot wide open. Likewise, the bokeh on my Zeiss 100/2 MP is pretty special (I believe this is a consequence of them not using any aspherical elements), despite the fact that it suffers from terrible chromatic aberration (possibly also related to them not using any aspherical elements). There's also color rendition of different lenses, but much of that can be corrected / simulated in post if you're patient enough. And every now and then I shoot with an old Zeiss Jena 200/2.8 lens with an adapter precisely because of its shortcomings yield a particular look. Colors are a bit more muted, it's a bit less contrasty, and chromatic aberration is extremely pronounced. It looks like a photo that would have been taken in the 60s, which is kind of neat.

Apologies for the long post! I love this stuff. :)

Edit: one more link. Ming Thein's review of the Zeiss 100/2 MP gives some more details on that lens, and I think some of the shots he's included are a great example of that lens's specific background rendering. Despite occasional annoying ellipses, it has a "swirly" property to it that I really like and I just don't get on any of my other lenses. https://blog.mingthein.com/2012/07/27/revisited-and-reviewed...