Currently, MongoDB uses geohashing with B-trees which will be slower than the R-trees of PostGIS (I can't give exact numbers, I'm afraid, but there is plenty of theoretical literature on the differences). However, in these slides, http://www.slideshare.net/nknize/rtree-spatial-indexing-with-mongodb-mongodc the author talks about adding R-trees to MongoDB and sharding on a geo key. You talk about desktop use, so geosharding may not be of interest, as sharding's benefits will be felt more on massive datasets.
Ultimately, it probably comes down more to what you want to do with your spatial data. Postgis has vastly more functions and support for topology, rasters, 3D, conversions between coordinate systems, so if this is what you are looking for, PostGIS would still be the best option. If you are interested in storing billions/trillions of spatial objects and just running basic find all points near/inside this point based on some criteria, then MongoDB is likely a very good choice.