If you are taking shots under certain circumstances, unless you have a side-side comparison (or even then) there would be
no way to determine the format based on a single image. Anything with low-aperture (high f-stop,) low-ISO, deep DOF is going to be almost unknowable at web sizes between micro-four thirds, aps-c, FF and even medium format.
If you find this surprising or reason for an 'ah-ha, FF is not worth it!' epiphany, then you
haven't been paying attention!
FF generally allows:
1) More noise control, if you are willing to accept less DOF for the same FOV and shutter speed, for example
2) More DOF control, for the same FOV and distance to subject (for typical non-landscape shooting, when a lens that has the same f-stop range.)
3) More DR above base ISO (with the same contingencies seen in #1)
4) Better performance with less-capable lenses when MP is the same or similar (as follows: the smaller the format, the better the lenses needed to get the same results.)
Unfortunately I very rarely bother to take/save direct comparison shots. As much as I talk about this, I probably should.
Anyway here's an example of a shot where FF gives two (perhaps) small advantages, neither of which can be seen at small web sizes and without a comparison shot - advantage 1) 20mm prime = 13mm prime on aps-c (none exists, afaik,) and 2) the 'sharp' advantage discussed in point #4 above.
Now here's an example of one advantage that could be seen even at web sizes if we had a comparison shot - this is 20mm wide-open at ISO 6400 - ISO 6400 on aps-c or m43 here wouldn't be quite as clean, and you'd have to rely on NR to match the perceived noise:
Here's an example of where some pretty extreme DR-shift was used in PP - at ISO 1100, the FF sensor used here had about a stop more leeway than an aps-c shot would have:
20mm ISO 2500 (DR example)
I think everyone has seen the DOF-difference examples many times from different sources, won't bother with them unless someone has questions.
Now the inevitable follow-up here is "well, I could have gotten the same thing with aps-c, look!" and then some other shot is shown. The real answer is
no you can't - if you were to take your example shot with two formats, you would see the difference as long as the circumstances challenged the equipment somewhat and not 'easy/indistinguishable' in the ways I laid out in the first paragraph.. You can take
very similar shots using anything between m43 --> medium format, but as you move up in sensor size you have more leeway, more options for getting better results.
.