There is practically zero difference between the two except perception. Point by point:
On the Youtube example, the viewers aren't stealing anything, so I don't really see how someone can be punished for that.
The same could be said for downloading music from P2P.
Now if someone ripped a track off of a Youtube video, be it audio, visual, or both, then sure, I could see a lawsuit of some sort happening because they actually "took" something, be it a file, a CD, DVD, something.
People doing a music download aren't "taking" anything, they are making a copy of it. That's why the lawsuits are for copyright infringement and not for theft.
The biggest problem with viewing things on Youtube is that some companies don't care what's on Youtube, they are cashing in on the publicity (and now commercials are being run during many clips).
The same goes for music. There is plenty of music that is freely published by the artist (or whomever holds the copyright) that is out there on the P2P networks or through MySpace or artist sites or where ever. There are also many labels that are not part of the RIAA and see free downloading as the best way to promote their work.
So unless there's a way to tell people exactly which videos are legal to watch and which ones are not (and of course the illegal ones would be taken down by the site), then there's really no way to prosecute the viewers.
The same holds true for music downloads. They don't come with warnings whether it is a work that is intended for the general public to download or not. It hasn't stopped any of the lawsuits so far. With music and movie downloads the industry lawyers have basically painted the picture that consumers should consider "all" downloads illegal when they are not. Even more confusing for the public, I can watch a clip of The Daily Show on Hulu or Comedy Central's site and it would be legal, but if I were to watch it on YouTube it would be illegal. Or even worse with networks now putting their own material on YouTube, watching a YouTube clip upload by HBO would be legal, but the same clip uploaded by BillyBob would be illegal.
And when stealing music, there's really no question that someone is stealing music. They are making a copy of it, so there is something physical, be it a file, CD, DVD, whatever. Really two different kinds of things here.
When you watch a video clip on Youtube that file is being downloaded onto your computer. When the video is over, the file is typically discarded. What most of the streaming capture programs do is simply write that file to a more permanent location. From the copyright owner's perspective they have absolutely no idea how to tell if the person watching a YouTube clips is simply watching the buffer copy or saving a download of the clip. The same goes for music downloads, the RIAA has very little idea if the music was ever burned to a physical medium, or shared with other users, or even ever listened to.
I don't think it will ever get to the point where companies will go after YouTube viewers (mainly because it is just easier to go after the hosts), but it is absolutely arguable that it would be within their rights to protect their copyrights in that way. The question still remains. If those companies felt that YouTube viewing was a serious threat to their income and the best possible way to put a stop to it was to make an example out of a few thousand people through lawsuits would you think that a $150K fine is excessive or an means to an end to deter the illegal behavior?
Bury me a Royal.