Youtube embedded player can be adjusted a lot using the parameters available here https://developers.google.com/youtube/player_parameters. Some parameters are available on both HTML5 and flash players and some are not.
Check out https://developers.google.com/youtube/youtube_player_demo, for all availabel configuration and play with it.
For example you can hide the controllers in embedded video, by setting parameter controls to 0
Default video quality can be set using vq.
Youtube allows you to have its logo to be modest, by setting modestbranding to 1.
We can also set all of these values together
