Startup time
First, startup comparison – judging by the time it takes for the lens to be fully extended, the Leica D-Lux 5 has a faster strartup time than the D-Lux 4 (on the video, the D-Lux 5 is on the right):
The D-Lux 5 is also much quieter – the sound you hear on the video is coming from the D-Lux 4.
AF speed
The new Leica D-Lux 5 seems to also have a faster autofocus compared to D-Lux 4 – I tested single and matrix AF and in both cases the D-Lux 5 was the winner: