this has NOTHING to do with your monitor's aspect ratio or size.
If the youtube player is 4:3, ALL widescreen content is cut or compressed or black barred.
If the youtube player is 16:9/10, ALL 4:3 content is stretched or black barred.
It will be like that in the small window, and nothing will change when you go full screen. Your monitor size and shape could affect the amount and size of the bars you see...but when viewing content that is not native to the player, there WILL be bars either way. This will be most horrific on videos that WERE widescreen...and had bars added to make it 4:3 for the old player. Now that its BACK in a widescreen frame, there are bars on all 4 sides.
...and yes...many, many videos will now be smaller on screen.
Get a clue and stop talking about who has what monitor.