Lots of members, including myself, have tried divided betta tanks. I used a divider frame from the pet store but put in that plastic craft mesh instead of the plastic divider the frame came with - the holes in the plastic craft mesh are a little bigger to allow for more water circulation. I think using the moss as a visual barrier is an good solution provided that you don't let the moss become too thick and obstruct the water flow. My bettas were always flaring at each other through the divider - probably a stressful situation for them long-term. Some bettas may stop flaring and some may not. The moss is worth a try and it will look nice too.
I encountered some problems that HeathB and BigJim mentioned. The divider frame didn't fit snugly and I had to adjust it almost every day. I worried if the sharp edges of the craft mesh would tear their fins. I tried to file the cut edges down with sandpaper. The mesh would often slip out of the divider and bettas can squeeze through small spaces. When one betta died, I removed the divider instead of getting another betta for the empty side. The main reason was the filtration and temperature. The filter (sponge filter) was in one compartment and the heater was in the other. In order to get a good flow of water across the divider, you need a strong filter, and bettas don't like current. I had a lot of algae since the water was somewhat stagnant.. The temperature was a degree or two cooler in the side that didn't have the heater. If you can get around these problems then you can have a nice divided tank. I only had a 10 gallon so it was difficult. If you have a 20 gallon, you can try to put a sponge filter and heater in each end of the tank.
