In R, you can access all GO terms associated to a species from the annotation packages:

> library(org.Mm.eg.db)     # install with biocLite('org.Mm.eg.db') first
> library(org.Hs.eg.db)
> mouse.GO = as.data.frame(org.Mm.egGO)
> human.GO = as.data.frame(org.Hs.egGO)
> head(human.GO)
  gene_id      go_id Evidence Ontology
1       1 GO:0008150       ND       BP
2       2 GO:0001869      IDA       BP
3       2 GO:0002576      TAS       BP
4       2 GO:0007264      TAS       BP
5       2 GO:0007596      TAS       BP
6       2 GO:0007597      TAS       BP

I am not sure what is the best way to compare two datasets from different species. The GOSemSim allows to compare set of GO terms from the same species, but currently the comparison between different species is not implemented. In any case you may read the GoSemSim documentation to learn about the different metrics to compare sets of GO term.

What about BioMart? I have never used it personally in this way but I know it offers a wide variety of annotations for many organisms (including GO terms of course). Its available here or here and also as an R package or python package.