Are Gutter Shut guards better than Leaf Guard?

Answer 1

No, not at all. While Gutter-Shut might work in a very light rain, it will shed a heavier rainfall directly over the gutters, making your gutters pointless. And in a light rain, where Gutter-Shut might work as designed, debris is not being washed down the roof anyways.
The mesh type Leaf-Guard is not all it's hyped up to be either. While it will allow more water to enter the gutter in a heavy rain than Gutter-Shut, the accumulation of leaves, twigs and debris at the gutter line can cause the same type of shedding effect and can actually cause the rain to back up past the gutter flashing, resulting in water damage to the sub-fascia and rafter tails. To maintain it's effectiveness, you will have to clean off the Leaf-guard periodically (but isn't this what you are trying to avoid in the first place?)
The gutter's main purpose is to direct rainwater away from your house to avoid erosion, water damage to the foundation and splash-back, which can ruin the bottom two feet of your siding. While using any kind of gutter guard might make cleaning the gutters less of a chore, if they negate the gutter's purpose, then whats the point? You may as well remove the gutters altogether.
My advice is to leave the gutters as-is. Sure, that means an annual or bi-annual gutter cleaning, but they will perform as designed and save you money in the long run. Cleaning the gutters is a lot less of a headache than having your foundation repaired.