There might be several reasons, and the first obvious reason is the target itself.

According to limited information in your question, following can be interpreted.

I don't know what 16S primers you have used but it might also have targeted prokaryotes. Another thing, COI is a functional gene. Do you know the copy number of COI in your target? Additionally functional gene amplification and library preparation is not as efficiend as 16S library preparation.

But in my opinion, it is not logical to compare the copy number of two separate target in metabarcoding assay. Another thing, you might not have run 16S and COI sequencing together, or did you? IF you did, 16S library have occupied most of the place in sequencing chip, thus higher number of reads.

The 2 pairs of 16S primers used in the study are specific for Fish and Crustacean, so that, theorically they will amply only reads from fish and crustacean, respectively. The COI primers are universal, they amplify for eukaryotic, so that, it is easy to reduce the number of reads assigned to Thyrsites sp. and Nyctiphanes sp. due to the existence of another eukaryotic reads in the dataset. As the study says: Taxonomic assignment for the eukaryote(COI) assay identified taxa from the phyla Ochrophyta (24.6%), Rhodophyta (17.5%), Chordata (15.8%), Mollusca (15.8%) and Porifera(10.5%).

Another point could be primer bias that under-estimate these genera or over-estimate another taxa, reducing the reads for the most abundant fish and crustacean.

Thank you José Francisco Cobo Díaz ! So more broader taxon coverage of a primer, less depth will be for single species estimate?

Yes, that is the reason for, in some cases, design specific primers for a genus, family or the taxonomic group you are interested in. There is also the problematic of primers bias. As an example, I have used two different ITS primer-pairs (universal for fungi) for the same samples, and some genera are only found with one of the primers, with a ... I don't remember but maybe around 5 percent of total reads, or even more.

Moreover, the lacks in databases could be another problem, I mean, if your genus of interest is not represented in the database you use (trust me, sounds crazy but sometimes it happens) it is impossible to find him.

Thanks José Francisco Cobo Díaz . Your Fusarium article was awesome.

Yes, I was aware of lacking reference databases. Thanks for your insights!