Big Green Brick? If so, it's very similar to the synthetic Blue Aoto I have.
I have the following suggestions:
Light pressure -- which is more or less true of all waterstones, synthetic or natural. These are NOT like Arkansas stones or similar oilstones that require significant pressure to cut.
Practice holding the knife at a constant angle to the stone -- those synthetic Aoto stones are very soft, and you will indeed dig gouges out if you are not careful. Took me a while to get the motion down. Getting a good edge off that soft stone greatly improved the sharpness of my knives, by the way, since I was also holding the angle better on other stones. Have a care to adapt to the different height of the stones, too, it's easy to use a different angle if the stone is higher or lower!
I suspect the Naniwa is similar to the blue one I have -- you will get a lovely, toothy but polished edge from that stone on softer knives ("cheap stainless" in KKF terms), but harder knives will feel somewhat blunt if you stop with the stone, and will require a finer stone to give a good edge.
Allowing mud to build up as you sharpen will result in a more polished edge than if you keep the stone clean as the abrasive appears to be friable, and will break down into finer floating grit and rolling/skipping free grit that polishes more than it cuts. I'm assuming the Big Green Brick is similar to the blue synthetic Aoto as I think it is (contains some natural stone ground to powder along with synthetic grit).
I've also been using mine on woodworking tools, but can't say at the moment if it is better than a 3000 grit synthetic stone, I'm still in the process of repairing severely worn plane blades -- they don't cut like knives, and most of the wear is on the flat side of the single bevel, resulting in hollowing out the flat side just above the edge. With severe wear from never sharpening, it takes an eternity to grind out the hollow and get a good edge. I cannot imagine how much effort it took to use those planes in the condition I got them!
Peter