Here is a
theoretical amount of blur as a function of subject-background distance for a full frame 50mm f/2.8 and an equivalent M43 25mm f/1/4 set up:
http://howmuchblur.com/#compare-1x-5...m-wide-subject
You can only see one line in the graph because the two lines go exactly on top of each other. So
theoretically the images should look identical in terms of their blur. Of course, the images will look different in real life because of 101 differences in lens and camera construction and signal and image processing involved. The formulas used in this type of calculators never take into account, for example, how many aperture blades there are, how sharp they are etc... etc... That's why an OOF light source is often rendered not as a perfect circle but as a polygon, "cat eye", "onion rings", "double circle" and whatever names people come up with. Same goes for tree branches against the sky and other high contrast subjects that are a challenge to blur in a pleasing way.
Would I be able to tell which photo came from a full frame camera and which came from an equivalent m43 set up? I'm sure some difference in the background blur will be easy to spot but might be difficult to link to a particular camera/lens combo. There might also be a noticeable difference in tonal range, micro-contrast and dynamic range - this is what I will be looking for first, not the blur. Though if you stick an old lens on a full frame camera and compare it against a shiny Zuiko that costs 10-20 times more, the viewer can be easily confused.