That'd be a "yes" on the game and a "maybe" on the Arkham style. Teenage Mutant Ninja Turtles: Out of the Shadows looks to me more like a modern-day update of the old arcade game, with four turtles beating up hordes of enemies. Either way, it looks fun, with unique weapons moves, double and even quadruple team moves, and Raph busting out a li'l pro-wrasslin' action. The turtle designs are based on the current cartoon, but done semi-realistically, which suggests an interesting visual twist (and, let's hope, more detailed toys, or at least game-based repaints).
After the jump, check out a loop of pre-alpha gameplay footage with additional information via commentary from IGN's Mitch Dyer and Rich George.