Can cork be used as a substitute for area rugs in an apartment?
Must also be comparable or better in noise-reduction because of downstairs residents.
Yes cork is a good substitute in your apartment. And yes it can be better in noise reduction.
Plus the different type of patterns and colors that are available will give you other choices.
For more information:
Read "Is cork as good for sound absorption as wall-to-wall carpeting?" a Q&A answered by Molly McCabe.