I'm having the same problem with Twitch as well. frames drop like flies. It's specific to Opera (appeared in Opera 45, wasn't there before), as watching in another browser (Sea Monkey in my case) doesn't create this problem.
Disabling Hardware acceleration doesn't make it any better. New Opera 46 doesn´t fix the problem, which seems to happen with 60fps videos.
Watching in full screen seems to make it more bearable, though.