Hi Clemence,
Some comments:
1) HUMAnN2 abundance outputs are in RPK (reads per kilobase) units. I.e. we normalize raw hits to the (alignable) length of gene sequences, which accounts for the fact that longer sequences contribute/recruit more reads.
2) The tool script humann2_renorm_table performs total-sum scaling (TSS) normalization. This can output traditional relative abundance units (sum=1) or the sometimes-more-convenient "copies per million" (CPM) units (sum=1e6). The latter form is equivalent to the idea of TPMs in RNAseq. (NOTE: CPM is sometimes used to refer to "counts per million" -- i.e. counts normalized by sequencing depth but not gene length. HUMAnN2 CPMs are always normalized by gene length.)
3) HUMAnN2 does not interact with RPKM units. Some recent work in the RNAseq field has demonstrated that a sample's underlying transcript length distribution can affect RPKM/FPKM units in a non-ideal way, and so TPMs are becoming the preferred measure there. We've adopted the equivalent CPM units for HUMAnN2.
4) Comparing relative abundance/CPMs/TPMs across samples is fairly common practice. While this approach is not without issues, I don't think there is a consensus in the microbiome field that another method is strictly better, though alternatives have certainly been proposed (including CSS, DEseq-style normalization, and genome-size normalization).