-Chat window that works well with touchscreen keyboard.
-Game score. There's number algorithms out there that show if you're winning or losing. There's not that many chess programs that feature this.
-Biggest preference is to allow simple screen tapping to move pieces. I tend to stay away from anything that forces you to slide the stylus since it will eventually chew up the screen.

I used to play speed chess quite a lot over at chess.net.

That was like ten years ago. I still consider myself to be a world champion though.