Different approaches imo. Coquelin's more action and highlights (no disrespect), whereas Arteta was better positioned. Arteta was really underrated. Could distribute well, defend well, and was usually in the right place.
I think Arteta did a solid job for us for a couple of years, then tailed off quickly. What's telling is his two best seasons came next to Song and Ramsey, both players who lack positional sense but can get up and down the park.
Arteta was tidier on the ball but Coquelin's attributes are crucial for us IMO. Although Arteta was sound positionally, a pacey CAM could always leave him for dead. Coquelin has good recovery pace and makes more interceptions.
I still remember our CL tie against Bayern in 2013, Kos scored late on and there was a real chance of a shock. Arteta however, continually fouled the Bayern players, kept taking the bait so to speak, wasted any time we had at a winner. I'm admittedly still bitter about that .