We designed GeoDesk with the assumption that users analyze/extract the OSM data with GeoDesk's tag-filtering/spatial operations, and then migrate the results to another database that matches their applications' needs. GOLs simplify distribution of OSM data. Internally, a GOL is organized into tiles (tens of thousands for a complete planet). With basic zip compression, these tiles are comparable in size to OSM-PBF (the most popular distribution format). As @pastage has already mentioned, converting OSM data into a GOL is significantly faster than importing into pgSQL (at least 20x). In the future, we envision that users will simply download GeoDesk tiles, skipping the conversion step altogether.
Another key difference is ease of development. GeoDesk queries return feature objects, obviating the need for object-relational mapping (For now, this is limited to Java and other JVM languages; we're considering a C++ port, which would pave the way for a Python API). GOLs replicate OSM object graphs, making it easy to explore the relationships between nodes, ways and relations: Find all residential streets within a city, count the number of speed bumps on each, find the crossroads, check which of these belong to bus routes, etc. All this can be done in pgSQL as well, but will require planning and proper table design to get it right.