Sorry, this is going to be a bit of a conditional answer, depending on what you want to do with your data. The tests you would use for presence/absence tallies of your genes will differ from what you use for abundance-weighted statistics. Which way you want to analyse them depends on your research question and possibly the difference in genome sizes between your groups so I won't give you an opinion on which you should do. If you want a demonstration of how you could perform these tests, I can show you the R code for any of them.

If you want to go with abundance-weighted my advice would be to just run sequential t-tests or Mann-Whitney u-tests across each COG/KEGG in your genomes and then apply multiple testing correction at the end. IF you want to visualise the differences between the genome structures (and maybe test up front whether there is a group-wise clustering effect) then I would recommend calculating the Spearman difference between each group and them use those distances as the input for either UPGMA (tree) or NMDS (ordination) of the samples. You would expect to see that the group A genomes cluster together and the B genomes cluster together without much intermixing.

If you want to analyse presence/absence the approach is the same, except that I would recommend a two-proportions test for the per-gene testing, and the Jaccard distance for ordination. The Jaccard distance is simply a measure how how many shared features occur between your two samples. It's simply 1 - (Shared features / total features), or if you're familiar with sets: 1 - (intersection / union).

I hope that helps.

Stefano,

I am afraid, that use of  COG and KEGG  classes in genome comparison (instead of direct measure of protein similarities) will cause considerable loss of information, until you compare very distant groups of bacteria. Generally, I support opinion of David - I would use the same methods.

Alex