Hamming code distance and error detection
Let's see. With parity, each block is 1001 bits long vs 1010 bit for Hamming code. So if the error rate is 0, then you economize 9 bits.

OTOH, if each second block fails, the in 50% of cases you will have to transmit a second block, in 25% of cases third block and so on. On average you have to send 2 blocks.

Now, let's go deeper. If the error rate is r, this means that each bit fails with the r probability. So, you can compute probability that there are k errors in the block.

You know that if there are 0 errors, you don't need to retransmit block, for a single error you need to retransmit parity-protected block, and for 2n errors you will got unrecoverable error.

Similarly, you can compute it for Hamming code protected block.