Somewhere on the internet . . . there is a US/UK government sponsored analysis that talks about the effectiveness of the defensive weapons, the different formations used, the different patterns of attack used, day vs night, etc. I do not know if I downloaded it, I will see if I did or if I can find it.
I do not remember all it talked about, but some of what I remember is:
Powered gun turrets were significantly more effective than free-swinging guns. The only location unpowered defensive weapons were effective was in the tail.
Prior to the introduction of the GGS: The .50 cal had a higher probability of shooting down or seriously damaging a Luftwaffe fighter attacking a bomber, if it scored a hit. However, the multiple gun .303 cal turrets, coupled with their higher rates of fire and increased ammunition loads, had a higher chance of scoring a hit. Exactly how effective the .50 cal was vs multiple .303 was difficult to determine as there was not enough specific information.
After the introduction of the GGS: It was clear that the .50 cal became the superior armament for the turrets, with the understanding that for future bombers the 20mm would be a significant improvement over the .50 cal.
In terms of the US vs the UK concepts as to the type of installation: It was found that the UK turrets, for the most part, were superior in terms of reliability to the US turrets. They talked about a number of items in the reliability, maintainability, service life, etc. The only 3 things I remember are:
1. US electric powered turret drives needed to be significantly improved. It was found on operations that a common complaint was the US electric turrets could become inoperative - often before reaching the target area - due to the weather conditions and overuse by the operator when scanning for bogies.
2. While the UK turrets (in particular the hydraulic drive types, whether in US or UK service) were significantly more reliable than the US turrets, the hydraulic type had the disadvantage of sometimes being the source of fires due to the hydraulic fluid being flammable.
3. The electric drive was preferred for future installation, because of weight and simplicity, if the reliability of the electric drive systems could be improved sufficiently.
Though it was clear that the larger caliber weapons were the best choice for future defensive systems, particular if GGS and radar aided FC systems were employed, the supply of sufficient ammunition was more problematic. A reference was made to US bomber crew complaints of running out of ammunition before the attacks were over, sometimes before reaching the target. Early-campaign, it was the tail gun position that usually ran into this situation, but the other turret positions also encountered this problem. Late-campaign - in the bombers that had increased ammunition supply for the tail positions - the situation of ammunition shortage was spread about evenly among the tail, top, and bottom positions. The nose turret was least likely to run out of ammunition.
The UK bombers, particularly the types with the feed track systems supplying ammunition to the tail from large bins in the center fuselage, seldom ran out of ammunition, and later in the campaign the tail turret ammunition was sometimes reduced or carried in a manner that would allow resupply of other turrets. (Note that the above applied to daytime UK operations. Night operations were different enough that they were included in a separate section comparing the day vs night operations.)
The introduction of the nose gun turret on the B-17 and B-24 had almost no effect on the attack methods used by the Luftwaffe, re the number of head-on attacks vs tail attacks only changed by ~2%, from ~43% head-on to about 41% (IIRC). Losses remained essentially the same for the Luftwaffe, as did the number of bombers shot down. This data was from Luftwaffe records and post-war debriefs of Luftwaffe personnel.