2 champions immediately came to mind when I read this.
can push really fast with his W, has strong poke with his Q, builds straight tank and still does damage, has some of the easiest last hitting in the game with his E and Q, and can 1v1 mostly anyone except high attack speed fighters.
is basically a melee ADC who can build both damage and tank items. He has a good amount of poke with his E. His sustain is just stupid with his W so he can push a lane or farm jungle forever, even if he just fought with an enemy champion and fell to 10 hp. Aatrox can 1v1 just about anyone in the game as long as he doesn't fall behind. The problem with him though is that if you do fall behind, don't expect to ever catch back up.