Did exactly this (up to Flaine from GVA) in March - Swiss side eminently better as:

1. Cheaper (often);
2. Easier to get the car from the airport - the French side is a trek from arrivals;
3. Quicker route out of Geneva up to Flaine - you simply drive direct through the border checkpoint, barely a need to slow down - the route from France involves a fairly convoluted journey around GVA;

Things to be aware of:

- Swiss law mandates snow tyres if travelling in Winter months, make sure included so you don't get stung with extra charges;
- You need a pass to drive on Swiss motorways - should be included with the car, but worth checking;

Swiss side = way to go.