The position that the first picture represents provides a more natural hand position, with a lot less strain for the wrist. Also, you are holding a thinner part of your partner's body (the hand) which is more ergonomic and therefore, easier to grip than a wide forearm (picture yourself trying to grip a small baseball or a big basketball, which is easier to hold?).
The second picture (forearm grip) is the exact opposite. The unnatural hand position and the awkward wrist strain equals a more difficult hold, partially loosing the ability to grip with the ring and pinky fingers.
Also, the first kind of hold frees the wrist, allowing more mobility, which might be useful in order to lift someone using an angle that is not straight up (let's say you are laying down on top of a cliff, perpendicular to the fall)
That being said, the only case I would see the second one being more effective would be when both of you have terribly sweaty palms and the contact of both of them together increases the sweating. But generally, I would say the first one is the best one, for the reasons stated above.
I didn't find that info in the internet, I'm just talking from personal experience (rock climbing and aerial silks)