From when I discovered 613Tube, I began to replace the all YouTube links to 613Tube before emailing videos to my friends and they all commented positively about it.
The Add-On's description is worth reading and says it all, yet one point I'd add to the description from my own experience now:
I find that the original YouTube itself became unnecessary to visit anymore. This totally takes over. Yet, the original YouTube website is still necessary in order to UPLOAD a new video, or to subscribe to a channel, etc. and those pages from YouTube indeed do NOT redirect to 613Tube. Cool!