If one were to adopt the first of the two perspectives on a GWAS study, namely that it is a formal statistical hypothesis test in its own right, then power comparisons become more complicated, at least under a frequentist statistical perspective: for a given nominal per-SNP significance level, the overall GWAS experiment will have somewhat different false positive rates for the different commercial chips, because they have different SNP sets, or when some SNP genotypes are imputed, depending on the number of imputed SNPs, for the same reason. Actually, even for a fixed chip, overall false positive rates will differ depending on the population in which the GWAS is conducted, because of differing patterns of LD between the SNPs on the chip (and hence different effective numbers of independent tests).
