Comment by aidenn0

The constant factor is different. If you want a small number of collisions, you will need a very small load-factor (you can't do most techniques for handling collisions because you aren't storing the key). So if you treat your hash-table as an array of bits and you run at a load-factor of say .1, then you are now using 10 bits per key, which is a lot more space than a bloom filter or an xor filter with the same false-positive rate.