I don't remember if the demo has these settings or not but I'm pretty sure it did, press "Esc" click "Options" then "Video Settings" and set "Use VSync:" to off and "Performance:" to Max FPS and try that.
You may want to adjust the render distance, smooth lighting and graphics also if the above don't improve your performance enough.
Also turning on Advanced OpenGL can help some people's performance but can also hurt other's (Like mine) so give it a try and see what happens.
Minecraft is one of my all time favorite games as with Mojang releasing new updates and the awesome modding community it never really ends.
If the demo version doesn't have these settings this gives you an idea of all the ways you can improve the full version if you buy it.
I hope I was able to help you out with this post.