For the uncompressed FASTQ benchmark, my relative timings differ from his, with Julia being ~30% faster. It's probably because he installed an old version of FASTX.jl, that would also explain his seemingly outdated comment about the FASTX.jl source code. Another 30% time can be shaven off by disabling bounds checks, which would put Julia as the fastest program on the list, around the speed of C. However, I don't think the speed increase is worth it, since FASTQ files are basically aæways compressed in real life.
For the compressed FASTQ file, it seems this is entirely explained by CodecZlib.jl being 2x slower than whatever his C solution is using. However, when profiling CodecZlib.jl, it just spends all its time calling `zlib` written in C (calling C has near-zero overhead in Julia). So I have no idea why his benchmark is slower there.