Why would anyone pay $10k more than Leaf - for essentially the same range as the Leaf and with 2 less doors ?
For many of the same reasons that people buy BMW 1-series instead of, say, a Toyota Yaris. For more reasons than people that buy an Acura MDX over a Honda Pilot. The LEAF will likely remain a larger seller, but there are a lot of people very interested in the i3 - including many that would not consider a LEAF.
By the way, after a month of ownership to learn the car's capabilities, extremely few LEAF buyers have range anxiety (and most of the ones that do are victims of the "100-mile" false advertising; it's not an inherent problem with the car, but like all cars it doesn't work for everybody - the problem is that some dealers - and even Nissan initially - were setting up the uninformed for failure. That's not just a Nissan problem; at some Tesla stores you will still hear product specialists telling consumers that the Model S is a 300-mile car, which is going to cause some of them problems as well; we've seen a couple of examples on these forums. Consumers can easily have problems with new technology when they are misinformed as to its capabilities; that does not mean the technology itself is bad). I know many LEAF owners, including close friends and my father; and I used to have a car with similar range. If you're going near the edge of the LEAF's range, just take the other car. Every one of them uses the LEAF as their first car and does the vast majority of their driving with it. It is not complicated at all; it's just like having a Miata for commuting and fun, and taking the Explorer on Costco days. We did it for years with 0 problems and no fear.
Sure they all WANT more range to cover those rare long days, as they prefer driving the LEAF to their gas car. But they can all do the vast majority of their driving on electricity, yet still get everywhere they want to go and they never have to sweat getting there. Plus...the i3 has an optional range extender! Not only does that make it less scary to go to the edge of the battery's range and less necessary to keep it fully charged just in case, but it also means that a single-vehicle owner that doesn't take many trips (even with the range extender it's still not a good car for lots of really long trips) could consider it as an only car.
Plus BMW has put a lot of serious thought in to using sustainable materials and processes for the i3. Not many people buy based on that criteria, but it will help a few pick it over the LEAF.
The i3 is not for everybody, and there's a lot more BMW could do to make it more appealing. But there are a lot of people out there that it will work very well for as-is, and most of them are going to love it more than any other car they have ever owned.
Heck, as much as I dislike what Toyota has done with the Plug-in Prius (and as many owners as I've encountered that bought them out of ignorance of the alternatives), I have even encountered some very thoughtful owners of that car did that a careful analysis and determined it was the best car for them. As frustrating as it is for me that automakers are dragging their feet on going electric, I am still VERY glad there are a range of cars available. The i3 isn't groundbreaking, but it still offers a few things that others don't, and that's good. Merry Christmas to all of us!