The stairs, properly cleaned, is by far the best option and has zero maintenance. Vinyl flooring is an unnecessary expense and tends to blow and crack, then becoming unsightly and dangerous.
Regarding noise, the stairwells acoustically amplify noise to nuisance levels that affect all occupants. A sign up in each stairwell requesting consideration of noise would be highly appropriate.
There are some benefits to the application of a new floor covering. Noise from footfall and general use of the stairwell reverberates and reflects from the hard concrete surfaces, and can clearly be heard within the flats. However the proposed vinyl would not provide any real absorption, and I feel the council would be reluctant to spend further funds on a floor type that would prove beneficial in absorbing noise. I have very little confidence in the workmanship and end result if such a floor was to be applied. I therefore agree that it is likely that we will end up with an eyesore if the vinly goes ahead, so would prefer a general cleansing/refurbishment of the existing surface.