from the series "how it feels to me"
The distance from my dominant (right) hand to the putter head has increased with the new cross-handed grip, in turn increasing the overall distance from my right shoulder to the putter head. The increased length, acting like a lever, creates a small amount of additional lag in the putter head. Although tough to see and feel, there is lag and release in a proper putting stroke. The lag creates a softer feel during impact. A small amount of give or shock absorption in the hands. I think it depends on the individual and their tendencies. If someone generally needs to hit putts softer, increasing the length will increase the lag, thus softening the impact on the ball.
Technically this does not make sense considering that increased lag in the full swing typically adds swing speed and ultimately more distance. But, that is how it feels to me.