I used to own a Sterling, and currently own a Stingray 5. This comment refers to Stingrays with the three-way coil selector. Both are fantastic basses.
The Sterling's SOUND differs in a couple of ways. As pointed out, it is a lighter weight body. Second, the pick-up is hotter and more "active sounding" than the Stingray. Therefore the sound is little more clear, edgy and aggresive than the Stingray. The three coil selections sound very distinct.
I find the Stingray 5 to have more warmth and roundness to the tone. The coil switching selections are less distinct, but the electronics are effective enough get aggresive when needed.
I initially went with the Sterling because of the Jazz neck. I sold it because of the lack of warmth and low end that I was looking for. The bass control seems to be voiced too low, just essentially adding rumble to the tone. The midrange was fantasic, however.
If I were to do a four string again it would be the Stingray because of the tone and pickup. I prefer the slimmer neck of the Sterling, but the Stingray seems to fit me better.