EDIT2: In the limit, if the number of hash functions equals the number of bits, then we can see that inserting one element would set all bits in the case where we use separate tables, but only 50% of bits if they use one big shared table.
So the false positive rate is higher if they use separate tables.
Related:
https://prog21.dadgum.com/29.html
Would a bloom filter be more or less effective if each hash function was given a separate bit-table rather than sharing the same one?
Seems to me that as long as the total number of bits is the same it makes no difference whether each hash function has a separate table or not.
EDIT: Although, https://chatgpt.com/share/6a67336b-8600-83ed-9671-fab769b485... - it is in fact ever so slightly less effective if you have a separate table for each hash function
EDIT2: In the limit, if the number of hash functions equals the number of bits, then we can see that inserting one element would set all bits in the case where we use separate tables, but only 50% of bits if they use one big shared table.
So the false positive rate is higher if they use separate tables.