Simply put, screen tearing happens when the Video memory buffer updates while the Monitor captures the image, "in-process" and produces two images on one screen. In high speed movement games, it becomes very visible, and distracting/annoying/ugly. This can happen regardless of using two different monitors. So if you just used your 144hz 1080p monitor by itself, you may still experience tearing.
Now, you can still use two different monitors 60hz + 144hz together. You might not like using them together for gaming. Half your screen would appear smoother than the other. Unless you duplicate the image on both screens. (That would be interesting for side-by-side comparisons.)
Some games (or game modes) can black out your secondary monitor, while the main action happens in the other. You could avoid this by "windowing" your game, and not using the "Fullscreen" option. Or if you prefer that, then leave it alone.
I think the best experience would be one144hz monitor in fullscreen mode. But if you use the 60hz monitor as a secondary screen, and not use fullscreen gaming on both, then that would probably be nice as well. Maybe have Firefox open on it showing game stats (Battlefield 4 Battlelog) or Game guide websites, etc. Possibilities are endless. Have fun!