The Model S P100D with Ludicrous mode is the third fastest accelerating production car ever produced, with a 0-60 mph time of 2.5* seconds. However, both the LaFerrari and the Porsche 918 Spyder were limited run, million dollar vehicles and cannot be bought new. While those cars are small two seaters with very little luggage space, the pure electric, all-wheel drive Model S P100D has four doors, seats up to 5 adults plus 2 children and has exceptional cargo capacity. (* Expected value using max power mode and Motor Trend benchmark)
The distinction as "quickest" is based on acceleration, not overall top speed.
The increased acceleration capability comes from advances in battery technology, which Musk also discussed. He said there will be a new 100-kilowatt hour battery option for both the Model S and Model x that will extend the range of the vehicles.