DxO has tested the latest Sony Rx100 II camera featuring 20.2MP BSI sensor with 2.4um pixels and compares it with the last year Rx100 camera with identical size FSI pixels. Sony says the new sensor is 40% more sensitive to light. DxO measures a more modest 24% ISO improvement. I'm not sure if ISO is measured just in the center of the sensor, or over the whole sensor area including sides and corners. Possibly, corners could show a bigger improvement due to a better angular response of the BSI sensor.
Update: Sony posted an Youtube video comparing the older FSI sensor with the newer BSI one: