These are some of the differences between EBI-GOA (QuickGO) and GO Central (AmiGO) when it comes to entities.
GO Central recommends that GAF annotations are made to genes, that is 1:1 equivalents. In GOA (and consequently in QuickGO) annotations are made to proteins, and there may be multiple proteins per gene, sometimes representing different isoforms. You will see this reflected in different numbers for mouse annotations for example.
This is a very important difference, one that users can see when comparing UIs, but more importantly, it is about the underlying datasets and whether a gene-centric or protein-centric worldview is chosen.
Additionally, GO Central omits the majority of the sequences and IEA [electronic] annotations from UniProtKB from the weekly database builds due to the large size of the data set. For those species with a dedicated authoritative database group, such as Drosophila, mouse or Saccharomyces, UniProtKB annotations are collected and submitted by the dedicated group, and hence the UniProtKB IEA annotations for these species do appear in the GO database. As an NHGRI funded resource, GO Central focuses on annotations that elucidate human genes or genes of relevance to human health in some way. GO Central also includes plants, as well as the 200 genomes of the "Quest for Orthologs" project. More datasets will be supported depending on available resources.
You can learn more about this subject at http://geneontology.org/page/lead-database-guide#why and at http://geneontology.org/page/download-annotations