Is there a noticeable difference between a 23.1 x 15.4 mm and a 23.6 x 15.8 mm sensor size when accompanied by a prime lens of 1.4F?
After how large a change in the numbers does the difference get noticeable?
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The aperture won't matter at all — f/1.4 will be the same in any case. Focal length could be considered to matter if you measure what you can fit in the frame with a ruler, but even then the percent difference due to different sensor sizes stays the same (which is why the concept of "crop factor" works).
This is super-easy to calculate because the difference is directly proportional to focal length. That means you can divide one dimension by the other to get a meaningful value for the difference. In the case you give, 23.6 / 23.1 = about 1.02, or a two-percent difference.
So simply put, the difference in this case is barely noticeable. If you overlaid two images taken from the same location you might be able to tell, but slight differences in position and framing — and variance in labeling of focal length — are going to be a much bigger deal.
You can decide for yourself what you consider a meaningful difference. 10% is probably enough that you can see it but it won't real make much difference. At 20%, you'll probably think, yeah, that matters.
I highly recommend you try the on-paper exercise I lay out in this answer on angle-of-view. In addition to the examples I use, also try the exact measurements for sensor size you want to compare, and this will become directly clear in a way that's going to be more meaningful than thinking about abstract numbers.