Re: 9' 8-weight versus 11' 8-weight (switch)?
With a two handed rod, you can move the upper hand (fulcrum) to the top end of the cork and leave your bottom hand at the end of the butt. The longer that distance it, the more leverage you have against the fish.
If you just hold the rod with one hand, the fulcrum is the forward end of your hand, and the force is applied at the back of your hand, a distance if ony a few inches.
The mechanical advantage is the proportional to the ratio of distances, less than 1 in both cases, but far higher for a two handed rod.
I am assuming you are not reeling, but using the drag on your reel.
The most advantage would be if you dropped the rod and pulled the fish in hand over hand.
Tie a small weight in a line that extends about 3 ft from the tip of a rod and move your hand or hands to check on the easiest way to pick it up.