I would rather push as it keeps me, and everything out of the falling path of the tree. The other thing too is, there is no attachment point. I have never used a tree felling jack, but when a wedge or two fails to send them over, cutting a "pike pole" out of a sapling usually works for additional leverage. Just cut a sapling 8 feet long or so, put it under a branch, branch stub, or anyplace it will get a bite, and thrust. The added leverage will send it over the center of gravity. When doing this, I do not thrust like a spear, but like I am cupping my hand giving someone a lift up. There is a lot more force by using your legs. On a tractor, bulldozer or skidder, pushing allows the person to back up out of the way as it is going over. On the skidder, I had an extra option. Most times it was easier to push them over with the blade because I could see better, and the blade is a big target to hit. But once and awhile, if the tree was really a leaner, I would back into it with the arch since the leverage was much higher.
Now hold on there... Sex is like pizza and star trek ... Even when it's not great it's still good. So you are going to have to qualify that. Better than store bought pizza? Sure... That's believable. But cmon bro you are losing all credibility with a blanket statement like that.