I own and shoot both. From the bench they shoot comperably. I have .243, and 30-06, barrels for both. Personally I prefer the Handi.
One big reason, I can close the Handi without making any noise. When I close the Encore, no matter how easy I try there is an audiable "thunk". When out hunting preditors often after the first shot the pack hasn't placed where the shot came from, or where I am, and will just freeze, looking around. With a Handi I can open partway remove the empty, replace the cartridge, and close the gun without making any noise that will give away my position. I cannot do that with the Encore, no matter how hard I try there is always that closing noise. They hear that sound and scatter.
Second reason I prefer the Handi, I hunt where sometimes my quary can kill and eat me. In the event I need a second shot, the Handi is much faster to reload. Think about it, upon opening the empty is gone with the Handi. All I have to do is drop in a new cartridge, close and fire. With the Encore, I have to physically remove the empty before I can drop in a new cartridge. In cold weather my old fingers get stiff and don't work that good with fine manupulation sometimes. That is time consumning, and could be disasterous for me.
Third reason, the Encore just does not feel right to me. It does not shoulder as comfortably as the Handi. One good test, close your eyes and get comfortable holding the gun down. Then with your eyes closed shoulder the gun, get into a shooting position, then open your eyes. You should be looking right through the scope or down the sights, without moving your head. I can do this with the Handi, not the Encore.