Youtube will remember your quality preferences across websites but will “default” to a setting that compliments the player size if no such preference is set.
However, that’s not the only concern bandwidth-wise. There’s also the thumbnails. Youtube generates different thumbnail sizes for videos.
mqdefault.jpg = 320px wide
hqdefault.jpg = 480px wide
maxresdefault.jpg = the actual size of the uploaded thumbnail.
Embedded Youtube videos in Discourse are 480px wide and the thumbnails are
hqdefault.jpg which again are 480px So this works well.
Now, if you use CSS to make the embedded player 690px or the full width of the post, you will “stretch” the
hqdefault.jpg thumbnail to the width of the player or 690px
Once the video starts playing this is no longer an issue but before playing the video you will have a slightly blurry thumbnail displayed due to the size difference.
So what then? Well, you could request the
maxresdefault.jpg thumbnail for the videos. Here’s where it gets tricky.
The difference between
maxresdefault.jpg can be pretty significant. While it’s not an exact science, expect something along the lines of x5 or even x10 the size of each thumbnail.
You can test this yourself.