The i3 is one of the best interpretations of the electric car, although it I guess it has been surpassed by now by the likes of the Renault Zoe and Nissan Leaf.
The i3 is what you get when you build an electric car that is optimized towards what an electric drive is good at _right now_. Given the range problem of the current battery technology, a short range city car with minimized energy consumption is where the electric drive is best at showing off it's benefits.
The Tesla on the other hand is what you get when you brutally try to hammer the electric drive towards matching the range that people are used to. It's a heavy machine that uses most of it's energy to hauling around it's battery.
And while, as you can grasp from what I wrote, I really like the idea behind the i3, it's obvious that the Tesla approach turned out to be better. It leads to a more practical and competitive car that is easier to sell.
The story if BMW i is a bit sad, as things didn't turn out that well. The idea was to make purely electric vehicles and built them sustainably (the interior of the i3 is largely made from some kind tree leaves if memory serves me right) - but BMW quickly figured out that they can't sell enough of them. Which is why they switched their approach towards developing vehicles that can either be built with an electrical drive train or with a combustion engine.
They basically have Teslas problem in reverse: Tesla can't build their factories fast enough to meet the demand for their cars, BMW can't build demand for electric cars fast enough to fill the production capacity they have (3 million cars per year).
(This reads more pro BMW as I mean it - I don't wanna say what they do is the best they could, I don't know that - it's more meant to try to see their point of view to understand why they do what they do.)