For particular QC-LDPC code and BCH code, you have observed the SNR gap between the two codes from the simulation results. There is no need to know the theoretical SNR gap between them. So, I guess that you are talking about the theoretical performance of an ensemble of QC-LDPC codes. In this case, you can obtain the average weight enumerator for an ensemble of LDPC codes at first, and then use it to calculate the theoretical BER upper bound. However, from my limited knowledge, it is hard to obtain such an average weight enumerator. You can find some research results for general LDPC codes, but I am not sure if they are applicable for QC-LDPC codes.