Which neighborhood is best for someone that doesn't own a car?

Both neighborhoods have their advantages in this case. Queens Village is very close to Old City and Center City, so close that when the weather's nice, you probably wouldn't hesitate to walk to these locations. This neighborhood also has some good restaurants and bars, and is close to other neighborhoods that have the same. Having a bike is very common in Queens Village!

Powelton Village is across the bridge into University City, so you're a little farther from Center City (about 10 blocks) and Old City (about 30 blocks). I'd think you'd definitely want a bike in Powelton Village, especially if you like going into Center City, or if you work in Center City. Powelton Village is near a great grocery store (The Fresh Grocer) and all of the amenities and spots in University City (restaurants, bars, movie theater), so you do have things up that way and wouldn't need to ride your bike to get to fun spots or to get groceries.