I'm in Chamonix several times a year and I always compare the French and Swiss side prices. Swiss is more convenient (toll sticker) and always more expensive, but which I choose depends on the price difference, which can be anywhere from 30-100%. There is a tremendous variation in Swiss rental prices from one weekend to the next, as Europcar, Avis and Budget all actively adjust pricing based on demand at GVA (just like the airlines!). The biggest negative of the French side in winter is no winter tyres, whereas all Swiss cars have them. Sometimes I reserve on both sides and cancel one based on the expected weather conditions a couple of days beforehand.