using 2 short CRC(s) VS one longer CRC

Question

I'm doing some research on the CRCs, but i can't find informations about the use of two (or more) short CRCs compared to the use of a longer CRC:

Suppose that i have a dataword A of some length and 3 different generator polynomials, 2 of degree 8 and one of degree 16. These polynomials are used respectively by CRC1, CRC2 and CRC3 algorithms, where CRC1 and CRC2 generate 8-bit codes while CRC3 generates 16-bit codes.

Suppose also that the three CRC have the same Hamming Distance for datawords of the same size.

now consider these 2 options:

1. Compute CRC1(A)=x1 and CRC2(A)=x2 and use codeword A|x1|x2 (where '|' means concatenation);

2. Compute CRC3(A)=y and use codeword A|y;

what are the eventual advantages and disadvantages of the first approach in respect to the second considering error detection capabilities?

Please provide also some references if you have them!