NOTE: I realise the above image may look a bit like a colourblind test; the squeeze bottle was the first and only thing that came to mind. Alas, I forgot that our pine floor hasn't yet darkened. Sorry.
APS-C’s biggest advantage over FF isn’t size. It is reach. An APS-C camea cocked into a 200mm lens frames subjects similar to a FF sensor cocked into a 300mm lens, but it can focus in closer to a subject. Similarly, an APS-C sensor cocked into a 35mm frames subjects similar to a FF sensor cocked into a ~50mm lens, and it nearly halves the minimum focus distance.
The smaller the sensor, the shorter the minimum distance from sensor to object necessary to frame the equivalent image of a larger sensor and longer focal length lens.
While it’s not fair to bring a rangefinder into this, I will make room for the Leica M. My only 50mm lens is the Canon 50/1,4 LTM, whose minimum focus distance of 1 metre keeps a good distance between the photographer and her subject. A 50mm FF SLR lens shortens that distance by about half. (The minimum focus distance of my Nikkor 50/2 Ai is 0,46 metres.) Finally, the XF 35/1,4 Fujinon nearly halves that; its closest focus distance is 0,28 metres.
Of course, you could crop the output image of a 35mm FF lens on a FF dSLR to roughly match the minimum focus abilities of its APS-C counterpart, but that adds unnecessary complexity to shooting. And it belies the merits of your system.
Below is a quick and dirty illustration of the minimum focus distances for the three lenses mentioned above. For each camera/lens combination, the squeeze bottle bee-lined in front of it sits at the minimum distance at which the lens can reliably focus.
NOTE: Each image was shot at a 1/1600 exposure setting at ISO 1600. The two FF camera systems were stopped down to f/2, though because equivalent framing isn't necessary, was a wasted effort. Apart from setting manual WB, no post processing applied to the below images. Fluctuations in light are the result of acts of God.
Leica: Canon 50/1,4 LTM: ~1 metre
Nikon: Nikkor 50/2 Ai: 0,46 metres
Fujifilm: XF 35/1,4: 0,28 metres
While shooting this close probably isn't all that necessary for a vast majority of photographers, it is an advantage for when you need to close into your subject. Of course, even smaller sensors and shorter equivalent focal lengths will get even closer.
I find the combination of the X-T1 and 35/1,4 to be incredibly helpful for natural light still life photography, e.g., the image set I took of the PlusSound Cloud Nine. I can get close, and thanks to the 35/1,4’s modern construction, can expect sharp results.