Thom Hogan has a really excellent article out
on lens and exposure equivalence between formats..
Here's his list of equivalences for a very similar image (exposure, DOF, noise, motion blur) - assuming all the cameras had the same pixel count. (Thom's are in bold - I've added a couple on both ends, which aren't bolded - errors there are mine)..
With large medium format (Phase One): ISO 6400, f11 at 1/125, 180mm lens
With small medium format: ISO 3200, f/8 at 1/125, 135mm lens
With full frame: ISO 1600, f/5.6 at 1/125, 100mm lens
With APS-C (DX) crop: ISO 800, f/4 at 1/125, 70mm lens
With m4/3: ISO 400, f/2.8 at 1/125, 50mm lens
With CX (Nikon 1): ISO 200, f/2 at 1/125, 35mm lensWith 2/3" (many compacts): ISO 100, f1.4 at 1/125, 24mm lens
With 1/1.7" (smaller-sensor compacts, oversize-sensor phones): ISO 50, f1 at 1/125, 18mm lens
With 1/2.5" (most cell phones): ISO 25, f0.7 at 1/125, 12mm lens.
For this particular image, almost all of the interchangeable-lens cameras are in the "sweet spot". Those lenses exist, diffraction won't rear its ugly head, and the ISO is reasonable. If you sized all the images to 20 MP, they'd look rather similar (opening the question of "why bother lugging the darn Phase if you're going to stop it down to f11 and be forced to ISO 6400").
The 2/3" sensor becomes hard to find the lens for (the ISO works - many premium compacts support ISO 100). Few if any compact cameras have lenses that open to f1.4, especially at a portrait focal length. There are a few that get to f1.8, only half a stop off.
The two smallest sensors require lenses that are
very hard to find. A few oversize-sensor phones have lenses in the f1.4 range, only one stop off, but that's the wide-angle lens - the telephoto is generally between f2 and f2.8. The "telephoto" may also not be long enough - many of them are around 50mm full-frame equivalent, not 70mm.
The f0.7 lens on the very smallest sensor is impossible to come close to on the market (it might be possible to build, but it would require enough of a camera bump that any sane manufacturer would put a larger sensor in there instead...).
Depending on the image, the right format could be anything... Let's say you like the look of street photography with the Olympus Pro 25mm f1.2 wide open on an E-M5 mk II. Another option is a Fujinon 35mm f2 wide open (it should be f1.8, but that's very close) on something like an X-T30, but that loses image stabilization. Getting it back requires an X-H1, which is much heavier. Another option is a Z6 with the 50mm f1.8 stopped down to f2.6, but that's much heavier and more expensive.
If you're willing to lose a shutter speed, the Fuji will let you have a stop less noise (both the Olympus and the Fuji start at ISO 200, but you either have to raise the Fuji's ISO one stop or lower the shutter speed one stop to account for the f2 lens). With the Nikon, you can either reduce depth of field farther by opening the lens up, raise the ISO or lower the shutter speed (or a combination).
If you want to keep your original shutter speed (so you'd raise ISO on the Fuji or the Nikon), the Olympus is the best way to get the shot.
A more extreme example (where Micro 4/3 is the only real way to get the shot) is Olympus' new 150-400 f4.5 Pro. It has a built-in teleconverter that makes it a 500 mm f5.6. The full-frame equivalent is a 1000mm f11 (or something faster stopped down to f11).
A 1000mm f11 exists! It's a 4" refracting astronomical telescope - and it makes a decent supertelephoto lens, if you can live with its limitations. Don't even think about autofocus (even variable aperture is relatively rare), and it's about three feet long, requiring a big, heavy tripod.
Another option is a catadioptric telescope, which uses mirrors to fold the optical path (photographers call it a mirror lens). A 5" should just about fill the bill, and it's not very big - but it certainly doesn't have AF (Minolta once made one that did, back in the film era), and it has really, really weird bokeh.
Of course, you could use the Canon 1200mm f5.6 stopped down to f11 - if you can find one of the 30 or so in the world, afford it (~$100,000), and afford the porters and tripod(s) required as well. A Canon or Nikon 800mm f5.6, cropping down to 1000mm field of view is slightly more reasonable (If your definition of reasonable includes a $13,000-$17,000 10 lb lens that's 18 inches long without the hood).
Or you could simply use the Olympus lens...
Sometimes it works out in favor of full-frame. The Nikkor Z 24-70 f4 is significantly smaller and lighter than its closest APS-C equivalent (the Fujinon 16-55 f2.8 ), and it has similar image quality even before you throw it on a body with twice the resolution! Micro 4/3 doesn't have a 12-35 or 12/40 f2 to compete, although there are certainly prime sets that can. Faster short zooms in general are hard to replicate on smaller formats, where the zooms tend to have similar apertures to their larger format counterparts, rather than the equivalent aperture.