Didn't the 8th AF publish stats on kill claims by gunner position? I can't find the information, but I believe it exists.
Cross reference that data vs. the percentage of hits from enemy fighters from each angle (meaning angle from which fighters attacked) and you get a very rough estimate of just how effective each gun position was - at least for the US heavies operating in the ETO.
I recall seeing stats which showed that tail gunners were the most effective, followed by top turret and belly gunners. On the B-17, the navigator's gun position was the least effective, to the point that it was often removed.
Going by the list of U.S. gunner aces (e.g.,
US Bomber Gunner Aces of WW2), where gunner positions are mentioned, tail gunners are most numerous, followed by top gunners and then ball turret gunners.
My opinion is that waist gunner positions were probably the least effective. They were single manually-turned gun positions with relatively limited arc of fire and very limited visibility which were usually making high deflection shots against targets maneuvering along multiple axes of motion (e.g., "beam attacks" from the rear flanks at the end of a "pursuit curve"). Although it wasn't well understood at the time, a bullet fired from a gun into a high speed crosswind suffers badly from "ballistic jump." While massive, high speed bullets like 0.50 BMG rounds are less vulnerable to this effect they still suffered from it. Additionally, bullets trajectories are slightly different when shooting at targets significantly above or below the shooter. Given that making precision shots on level ground at 300+ yards/meters in a high crosswind is tricky even for a well-braced shooter it must have been nearly impossible to get a good grouping while shooting from a standing position inside a vibrating bouncing aircraft flying at 200+ mph while trying to hold the gun steady against the slipstream.
Gunnery schools of the time didn't get into the ballistics required to get consistent hits and ignored factors like altitude (thinner air means less drag on the bullet and also slightly reduces gravity, it also has the illusory effect of making distant targets seem closer unless you have a frame of reference to judge the target's size), temperature (colder air increases drag), and the required angle of "holdover" required to hit much higher or lower targets.
Another factor is overall visibility from the gun position. It takes a gunner a moment to "acquire" a target and to judge its distance, speed, and vector before firing. For high deflection shots (i.e., a target flying along very different vectors from the gunner's aircraft) the ability to "track" the target prior to opening fire is vital. That corresponds to powered turrets with wide fields of fire like the top and belly turrets on the B-17 and B-24.
At night, visibility is crucial. Against the blacked out terrain of WW2 Europe, it was very difficult, if not impossible, for gunners to detect aircraft below them. In particular, it's very difficult to track dark objects moving quickly against a dark background, making high angle deflection shots almost impossible. Again, that favors gun positions with wide angles of fire, but with the added requirement that the gunner had to have something which would silhouette the target - like a burning city or light reflected from overcast or undercast clouds. It's no surprise that the Luftwaffe preferred to attack night bombers from below. It's also no surprise that the tail gunner was the person best positioned to see enemy fighters sneaking up from below and behind, since he would have a longer period of time to track a potential target.