Focus on the target vs focus on the cross hair -
Maximum accuracy will be achieved by focusing on the cross hair. Maximum speed (for me) is achieved by focusing on the target.
Basic marksmanship, with both rifles (carbines) and pistols calls for proper alignment of the front and rear sight, and focal concentration on the front sight itself once the relationship to the rear sight has been established. The relationship of the front sight to the rear sight, and the front sight to the POA are paramount because any error in alignment results in significant deviation as the distance grows. The use of a magnified optic is simply replacing the FS / RS with a single cross hair. Moreover, if one is fractionalizing the stadia in order to make holds, one must concentrate on the exact portion of the stadia that represents the desired amount of hold.
That said, focus on the target has its place. Its place rightfully comes long after one understands and enjoys a strong command of basic marksmanship. Focus on the target is advocated strongly for in some situations that are common in defensive pistol shooting - where it is known as 'point shooting'. This is the extreme - the shooter is only looking at the target and is aiming the HG simply by means of indexing their body to the target (never looking at the sights).
In a similar but more mild manner, one can simply look at the target to increase their speed with a rifle. This is esp true with red dot sights and 0 or 1x magnification. Most folks find it fastest to allow their brain to process that the dot is on the target as they break the shot, but without ever actually shifting their focus from the target to the dot. This is the same as the Binden aiming concept behind Trijicon and ACOGs. The same can be carried over to a precision rifle, however things can get messy quickly if the distance is substantial and the shot requires hold offs.
As has been said here many times before, the best thing to do is to become proficient with iron sights first. Then apply those same concepts to a magnified optic.
