AndrewBurns If I had to guess, LBRY. It's got the biggest user base outside of Youtube (as far as I know) right now and solves a lot of problems that people complain about with YouTube. That said, it's still lacking some things (video trans-coding, good analytics for content creators) that are basically required at this point in my mind. Still though, I'm happily using it most days for my Linux-ey videos that I used to get from YouTube and it works just fine.
Peertube - I don't see it growing since most people won't want to worry about hosting videos themselves.
Bitchute - Maybe, but it needs more users.
Vimeo, Dailymotion, Metacafe - These have been around a long time and will probably stay right where they are without growing or shrinking.
Obviously, these are just my opinions and speculation.