I've never played those games. My experience is limited to the various editions of D&D.My problem here is that D&D Next isn't even close to Dungeon World at any of those three things and 13th Age leaves it looking half-baked at two of them - and that's only when we stay under the D&D umbrella.
I will say that those three things, in my opinion, provide a vastly better tabletop experience than that of 4th edition and 3rd Edition and its variants. If you'd like to discuss D&D Next compared to the previous two editions we can.
Did you mean to say squares? What is better than real-world measurements for Theater of Mind?A game that measures areas of effect in feet is not good at theater of the mind at all.