you know... i've never really tried to load a video with an embedded youtube window and then swap to another one while it loads. the loading times usually are fairly quick so i dont have to do this.
it could be that your browser doesnt support this. perhaps try dolphonHD, opera, or another one of the different browsers. or perhaps the stopping is built into the mobile versions of youtube.. i'm not really sure
you cannot compare mobile and desktop versions. they are built for different purposes.
or open youtube videos in youtube. that might work in the background while you browse. yes.. open it in the app not on the website version.
if you want to listed to music while you browse the web i highly suggest pandora radio, slacker radio...