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I've been experiencing the same issue for a few years now, and I believe I know the cause. AMD cards cannot synchronize the display across different screens when using HDMI or DVI, or when using DisplayPort for one screen and HDMI or DVI for the other. The only way to synchronize the display is to use DisplayPort connections for all screens.
Read AMD's article about it here: Screen Tearing with Multiple Displays
So you have three options: switching to Displayport if your screens support it, getting a card from the competition, or continuing to switch the preferred screen when needed. Personally, I've set the preferred screen to the one I use most for gaming and video, and I try to ignore the tearing on the other screen (I use two screens total). Not exactly an ideal situation, but there you have it.