I can tell you right now, I have the Black Bow of Pharis +15 and Composite Bow +15 on a 28/40 build. With Large Arrow equipped, the Black Bow of Pharis has an AR of 408, while the Composite has an AR of 439. Feather arrows it is 380 to 417, respectively. The weapon upgrade/scaling breakdown is where the difference is apparent. The Black Bow has a much lower base damage rating at +15 (85), with extremely high scaling numbers (295) with S scaling in Dex and E in Str. The Composite bow has a higher base damage rating at 137, and with C Scaling in both Strength and Dexterity the scaling equals to 280. Remember all of these numbers are based off a 28/40 build, and I only went to 28 Strength for the Murakumo and Greatsword, it doesn't really effect the damage in either bows.
Gough's Greatbow even has a lower AR than Black Bow and Composite, but it has stronger arrows that supplement the damage. It's not really necessary to compare the greatbows with regular bows since there is such a disparity in weight. Trust me, I and many others have been using the Composite bow for a while now on Quality builds, and nothing beats it. Try it out yourself.