The main change targeted the lower toolbar. It is now smoother and offers only the option to switch to full screen, unlike the old player that also had a button to reduce the size of the video. The new player shows the vertical sound adjsting option that is displayed only when you hover the sound icon and at the end of the play there are minor adjustments on the way the share/replay options are shown (and the next/previous videos in the list).
It looks better, they've simplified the new player a little and that's good. Unfortunately for now if you have created Custom Video players for your website/blog, you cannot adjust their look based on the new YouTube player look. Probably that will change by default when the new video player will be the default one.