I think the only way to do this sort of comparison is to shoot the same subject side by side and as quickly as possible as seconds delay can mean changes in light and colour and contrast at equivalent focal length and apertures. Alter any of those things and the differences could be obvious and even with a just about perfect comparison I bet people will look for clues.
Actually, it's one those rare occasions where I'm not that interested in scientific comparisons.
I make photographs of a fairly narrow range of subject matter and I have files from 1", M43, APS and FF cameras of various ages and resolution. Including regularly photographing the same few sites (and the same subjects) and it's the difference in "feel" between the formats that interest me and I'm not sure how to measure it.
Some of the sharpest and perfect colour and contrast prints I've made came from my Nikon 1. For example, I had been taking pictures at a falconry display with a Nikon 1 v2 with the 70-300mm lens alongside a Nikon d7000 and an 18mm - 200mm lens. I was blown away at how good the Nikon 1 was, but there was something "nicer" about the D7000 images.
it wasn't noise (both had similar noise, after de-noising), but I like a bit of noise, and it wasn't sharpness because the Nikon 1 was clearly sharper than the Nikon D7000. The difference was in the colour gradation. On two pictures of the same Kestrel, on a perch taken one after the other, the Nikon D7000 print showed multiple subtle shades of brown and black compared to far fewer shades of brown and black in the Nikon 1 print.
The more I looked at the prints, the more the initial "wow" of how good the Nikon 1 result looked, gave way to me feeling it was rather harsh compared to the Nikon D7000 print. It wasn't something I could fix in processing, because the smaller file just didn't contain the information needed to match the results. As an aside, I found that making customised camera profiles with LumaRiver, gave small improvements n colour gradation across all file formats. But I've changed cameras since then and can't be bothered with the work involved, for only a small improvement.
It's an experience I've repeated over and over again, and overall the larger the sensor, the "nicer" an image feels. And while I am happy enough with results from all the sensor sizes I use (or used), I can't get away from the differences between them both when processing the files and in the final output.
However, I'm not that interested in a comparison based on minutia, or consciously looking for clues like different depth of field etc, I'm interested in the broad brush "feel" of the image.
How important this is, depends on multiple factors, sometimes it feels important and sometimes it doesn't.
And I confess, that over the years, I have in fact done far more testing and comparisons, than has been good for me.