There certainly is a point where "more camera" doesn't buy you "better image". Part of it is resolution, while dynamic range, noise, color quality, etc. also figure in. If it were just resolution, you wouldn't be able to tell any camera sold today apart on any screen readily available today (you certainly could on a print). The highest resolution monitor readily available (the 5K screen in many iMacs and occasionally found separately) is under 16mp, and, once you account for menu bars and other interface, probably displays (roughly) a 12 mp iPhone image - you can't buy an interchangeable lens camera below 16 MP, and haven't been able to for years.
Since factors other than resolution matter, it's relatively easy to spot that iPhone image on screen, even without a super-resolution screen. iPhone hallmarks include very poor dynamic range (or noise associated with computationally enhanced dynamic range), high noise, auto-editing and very specific lens choices (modest wide-angle and sometimes a portrait lens). Exposure is purely automatic, and may or may not match what a photographer would have chosen for artistic effect, although it's often close to technically correct. I can generally pick out a phone image of most subjects even at web size, if the subject is at all challenging or the "alternate" real camera image has any degree of creative choice involved (and I'm sure most photographers can).
Once you get clear of a phone camera, more and more cameras become tough to tell apart on a screen as you get more recent (without magnifying beyond what the screen can show) - a print is always going to be easier to tell than on screen, and a high resolution screen will be easier than a web image. I'm picking cameras I have known well over the years here - holding the Z7 constant because it's the camera with the highest IQ I've got more than a few shots on (I've handled a Phase, but never shot one seriously in the field). If you prefer Sony, please feel free to substitute an A7rIII where I say Z7 (or if you prefer DSLRs, throw in a D850) - they'd all be VERY,VERY hard to tell apart on screen, and so would a GFX or an X1D...
1.)Nikon D70 vs Nikon Z7? Easy - the resolution is a giveaway on a high-res screen, and the D70's color is nowhere close to what a modern camera can do (and is weird enough that it's hard to edit to look like a modern camera). The dynamic range is a huge difference, and many shots will show it - but you probably don't even need it. At web size, the color would still give the D70 away.
2.) Olympus E-M5 (original) vs. Nikon Z7? Both outresolve your screen, and the Olympus color is really nice, both are editable to look similar. Dynamic range is a giveaway in many shots, but if the scene fits within the Olympus' DR, it's hard to tell. There will be some noise in the Olympus image even at base ISO, and you can see it on screen if you look hard at a 4K or better display (no, it's not noticeable at web size unless the ISO is really high).
3.) Fuji X-T2 vs. Nikon Z7? This is very darned hard without a good-sized print (or pixel-peeping at 1:1). In a high DR scene, the Nikon will stand out, but the Fuji's colors are at least as good (and it's trivial to edit them to match). If you don't have enough DR in the scene to get the Fuji to blow a highlight or block a shadow, you'll never see the Nikon's extra 2 stops (at base ISO for both - note that they don't have the same base ISO). The other possible spot on a very high resolution screen if you really stare at it (think iMac 5K from a foot away) is that the Fuji has traces of noise even at its base ISO of 200. The Nikon doesn't at its base ISO of 64. At web size, they are extremely difficult to tell apart unless the Nikon's DR saved a highlight - you'd never spot the noise from the Fuji.
These cameras represent a pretty fair selection of digital ILC history - the D70 had a 6 MP CCD sensor that is a good representation of early-generation digital, the Olympus represents a whole generation of ~16 MP cameras from about 5 years ago, and the Fuji is a very good, modern camera with image quality very similar to what dominates the market today, with better lenses than many. The Z7 (along with the D850, A7rII and III and GFX line) is the state of the art as of early winter 2018, at least if you aren't willing to spend $20,000+ on a Phase One system. I'd love to have a 12 MP CMOS camera in here - it's the missing generation - but I never owned one...
We are also approaching a hard limit in useful resolution (technically, we aren't there yet, other than the Phase One IQ4 150). Estimates of the resolution of the human eye with perfect vision range from 130 MP (the central 45 degree section we concentrate on) to 576 MP (including our peripheral vision). To take full advantage of that 130 MP central resolution would involve looking at a 24x36" print from about 4' away, concentrating intently. From 6' away, you couldn't possibly tell the resolution of a ~50 MP camera from the Phase at that print size. From 8' away, you couldn't tell a 24 MP camera from the Phase on a 24x36" print. With a larger print, you can stand farther back to have it fill the same angle of view (or you can look at a smaller print more closely). Once you get above 130 MP, you can't get the whole print into your central vision from any viewing distance that would use the resolution (no matter the size of the print). This is pure line resolution - color vision is less acute than that, and anybody with less than 20/20 vision has less acuity than that.
We are probably between two and five years from a reasonably priced camera that outresolves our eyes even in perfect conditions - Fuji is introducing one that comes close this spring for $10,000 with the GFX 100S. A 24x36mm sensor using the pixel pitch of the popular 20 MP 1" sensor (Sony RX100 & co.) would be close to 150 MP - more than enough to reach the resolution limit. Using current technology, it would not be an acceptable high-end sensor in other ways - it would have similar dynamic range and color characteristics to a 1" sensor.
One place where we have already passed the resolution limit of the human eye is that some modern 4x5" films are past that line - there is no reason any more to shoot 8x10" for the resolution, whether for contact printing or billboard enlargement. 8x10" still has different depth of field and adjusting movements can be easier, plus it's useful for contact-only processes like platinum or palladium printing - an original 8x10" negative spares the step of making an enlarged internegative for an 8x10" print.
Of course, that's just resolution - the human eye can see a range of colors no camera can yet capture, no monitor can display, and no printer can print (there actually are color spaces that can store it). Our eyes also have 20 stops or so of dynamic range and, again, no mechanical form of reproduction is close (a few digital cinema cameras claim 16 stops, but nobody can project or display more than 10 or 11, so those 16 stops have to be brought down, by gamma curves and other editing, into the projector's range).