Personally I would never use #2. It reduces the shooters ability to control recoil and muzzle flip.
Ive found just the opposite to be true, and have much better control over both using the thumbs forward grip/isosceles stance.
....you want as tight of a hand hold you can get on a gun to reduce the time to get the gun back on target.
The thumbs forward grip puts "meat", on the whole grip, with no gaps or spaces in your grip. The #1 grip does not give this, as there is a gap under the left hand due to the right thumb not allowing the left palm full access to the grip. With a thumbs forward grip, the gun is locked in your hands, with very little movement.
I used to use the grip in the first pic, mostly back when I was still using primarily a Weaver stance, and still use a form of it when shooting one handed (thumb wrapped down and tight).
Im always open to trying new things, if it looks like it might have some benefits. Once I gave it a good try, and understood how the thumbs forward grip worked, and how well it worked, and got over the initial odd feel of it, I quickly came to like it. I find I recover from recoil, and come back onto the target much quicker, and with more "natural point of aim" using this method, than any of the others Ive used previously.
Is it perfect, not at all. Standing still, pivoting at the waist, it works great. Moving, well, sort of, depending on how your moving and where your shooting while youre going. For me, I can use it to shoot from straight ahead, to about 45* to the right, but shooting to the left, I tend to move into a modified Weaver or even more so, go to one hand.