There are obviously differences between Full-Frame and Medium Format, otherwise people would not be paying so much more just for a heavier camera.
Those who know can recognise the difference but that depends on the photo and most importantly the size at which it is viewed. In theory, one of the main difference is depth-of-field but since lenses are not the same on both for types of camera, you often have access to wider apertures on full-frame than on medium format, which cancels out much of the differnce.
The one difference that really stands out to my eyes is dynamic-range. I have shot architecture around me with Medium Format, Full-Frame, APS-C, Four-Thirds and even smaller sensor, so I have a good amount of images that I can directly compare. The Fujifilm GFX 50S for example captures such high dynamic-range that its outputs looks very similar to properly-done HDR.
Resolution is also very high on Medium Format, although the difference between Full-Frame is not that much. There are full-frame cameras with virtually the same resolution as Medium Format ones. This is mostly visible on very large prints but even when resolution is nearly the same, Medium Format will produce better pixels with lower-noise, more dynamic-range and refined colors. Again, this will not be noticeable on any image but it will on some.