By full screen, do you mean run a game in full screen? One limitation is you have to run games as Windowed or Windowed Full Screen. I open Xsplit, set a screen region by clicking top left of screen and dragging to bottom right. Then it only shows your screen as a tiny portion of the screen, so you hover over the bottom right corner to resize and stretch it. I did it all through Twitch.tv and it just worked like that. You may want to give it another shot.
Another option that I haven't tried, but saw on Twitter, is called OBS (Open Broadcast System) I believe. It advertises no limits on video quality, and it's free and open source. Could be worth checking out if you can't get Xsplit working?