Did another test of recoil out of relatively the same gun. A DDM4 RIII with a 11.5" and 16" barrel. Everything else is the same, Aimpoint PRO, Huxwrx QD 5.56 Ti, Magpul BUS, etc. The 11.5" weighed in at 7.95lbs and the 16" was 8.56lbs. The difference in weight is primarily the barrel, handguard (12.5 vs 10.5), and gas system (carbine vs mid length). 

Ammunition tested/used was IMI M193 and Speer Gold Dot 75Gr 223 Remington. The 75Gr Gold Dot contains around 26Gr of powder, the M193 27.6Gr. Out of the 11.5" the Gold Dot averaged 2,231FPS and the M193 was 2,716FPS. Out of the 16" the Gold Dot averaged 2,470 and the M193 3002.

Recoil impulse calculated in order of lowest to highest in FPE. 1.19 for the Gold Dot out of 11.5, 1.24 for the M193 out of 11.5, 1.33 for the Gold Dot out of the 16, and 1.38 for the M193 out of the 16. Both rounds had a lower recoil impulse out of the 11.5" then the 16".

Recoil velocity calculated in order of lowest to highest in FPS. 4.83 for the Gold Dot out of the 11.5, 4.99 for the Gold Dot out of the 16, 5.04 for the M193 out of the 11.5, and 5.18 for the M193 out of the 16. So the recoil velocity is lower out of the 11.5 in a given round, but comparing different rounds in different barrels can cause variation in which has a lower recoil velocity (M193 in the 11.5 has a higher recoil velocity then the Gold Dot out of the 16).

Free Recoil Energy calculated in order of lowest to highest in FPE. 2.88 for the Gold Dot out of the 11.5, 3.14 for the M193 out of 11.5, 3.3 for the Gold Dot out of 16, and 3.56 for the M193 in 16. So again both rounds are lower in the 11.5.

It's fair to say that in these examples, the 11.5" barreled gun has less recoil with a given round then the 16" barreled gun. Comparing different rounds can cause at least some altering in recoil velocity. 

This is just a couple of examples and how recoil is perceived is a different matter. Like a mid length gas system cycles differently then a carbine and short barrels can produce more noise and flash. Doing the testing, it felt like the Gold Dot out of the 16" had the most recoil, but on paper it was the M193 (but I shot the Gold Dot out of the 16" after the M193 out of the 11.5", so the contrast may have been more noticeable then shooting the M193 out of the 16" next).

In general its a good example of how shorter barrels can recoil less. 

11.5" vs 16" Recoil