Until recently, I used an AMD HD4850 graphics card, one output of which was connected to the monitor, and the other to TV in clone mode. Everything worked well. And my friends gave me a wonderful (no joke) Gigabyte Radeon HD6850 GV-R685OC-1GD video card , which I connected in the same way. A very unpleasant tearing effect appeared on TV. The effect is stable, it does not depend on the player or the output programs, it just is always there. Digging on the Internet has led to numerous discussions of the problems on the forums, a solution fortunately is there and it turned out to be quite simple - you just need to change the primary output on TV. At the primary output of this effect is not, but on the other, this may occur apparently some kind of magic synchronization / desynchronization signals. On the monitor, I practically do not watch the video, so I simply do not notice teraing there. In order to have a normal picture on the monitor, you can add a profile in Catalyst and switch the primary to this place if necessary.
However, the fact remains that something in the output signals of the new video card was different, before tearing was not on both outputs.