I've used both methods. I like the rod better than the clam shell deal. I also have the magwell block that clamps in a vice.
They all work fine as long as the torque is not excessive. Plenty of grease for the barrel and nut threads will avoid having to use a 5 foot lever to loosen it.
One benefit of the rod and magwell vice block is not having to remove all the accessories (optics) from the upper rail, which can keep your optic from losing zero. That assumes your optic isn't mounted above or forward of the barrel nut. I think most clam shell products need the optics removed.
Also, the rod lets you slide the upper on vertically, horizontally or any angle in between. You can easily rotate the upper to get a better angle on screws, gas blocks, gas tubes, roll pins, sights and so on.
As for potential damage, the magwell block always struck me as risky. I know the aluminum upper is strong, but what if you want to work on polymer parts? What if the part has the start of a crack and you are just stressing it more? Seems like the steel of the barrel extension makes the most sense when using potentially significant force in a twisting direction. As for clam shells, clamping anything around the outside of the firearm is just asking for gouges and wear on the finish. Besides the aesthetics, the finish is what keeps metal from becoming rusted metal!
If I had to choose one, I'd go with the rod. It's not only a great tool, but it's hefty enough to use for SD in a pinch, too!

I bought the Botach substitute for 1/5 the price of Geissele version at the time.
KZ Barrel Spline Socket Rod For AR15/M4 Upper 5.56mm Receivershttps://botach.com/kz-barrel-spline-socket-rod-for-ar15-m4-upper-5-56mm-receivers/#tab-reviews