Game capture is the preferred capture method, since you record the game only, no clutter from your desktop. If the game isn't refusing to be game captured, use game capture. Some games refuse to be game captured, in this case you need to fallback to window capture or display capture.
If it comes to performance, game capture and display capture is not really different if you use Windows 10. On Windows 7, display capture was awfully slow, but this isn't the case with Windows 10 (and probably 11) any more.