Two and half years back I was exactly in the same dilemma - chose between Figo and Punto, Figo being my first choice.
Finally went with Punto because of following reasons mainly (I think 1st one was sufficient, but...):
1) My wife liked Punto.
2) Ground clearance - I know at that time Punto too had this issue and only since I was going for top end (with 15" wheels), I was somewhat inclined towards Punto. But FIAT came up with increased GC for Punto 2012 and that issue was gone. I especially wanted the GC issue to be sorted since my travels would involve 5 elders in long journeys and didn't want different scrape behavior based on load.
3) 60:40 folding - I am not sure but guess Figo didn't have it then
4) Rear seat comfort and leg space - (possibly contrary to majority belief,) we felt Punto had better offering on this front compared to Figo, especially for under thigh support and accommodating 3 adults.
5) Steering mounted controls, alloy wheels, all power windows were other things which scored for Punto then but IIRC Figo also added ally wheels by the time I had finalized.
While, the most important thing in favor of Figo (which was my first and only choice actually) was that it was a great package on the whole available for best price!
Note that, engine, stability, driving pleasure wise I didn't have any issue on either with Figo additionally providing:
1) Best VFM
2) A lot better view for driver
3) Feeling that I was driving a petrol car (though this may put off diesel engine lovers) - I thought would have been easier for my wife to drive Figo than Punto.
4) Boot space looked better than what Punto offerred.
5) Ford as a company looked more serious about their base in India compared to FIAT (Note: I am not just talking about ASS
here, they are same everywhere except perhaps for Maruti/Hyndai), so that they wouldn't desert their products/roadmap etc just like that.
6) I thought Figo would have better resale value, mostly because of above point.