Coupe. My DD has the Coupe and my great-niece has the power car. The car is a hazard - kids run each other over, it tips on hills, and when the batteries run out, the kids get cranky. We also had to stop the kids at the recent party from "fixing" the dead car.
The Coupe may also tip on hills (so watch her) but never runs out of batteries and you have more control over it (not speeding down the sidewalk). I also think that kids can get more out of a car that requires them to push it - more exercize.
The power car is fun for my DD to use now and then, but she has no complaints about her car and has never asked for a power car. The coupe also holds up really really well. The only thing I'd change about ours is the handle, but it sounds like you will have one. :)