What has more muzzle rise on an AR-15, 16" barrel or 11.5" barrel?

I recently got into a debate among other shooters about which barrel length experiences more muzzle rise, a longer barrel or a short barrel? The debate was between a 16" barrel which is my go to rifle and my soon to be built 11.5" barrel. I speculated that a shorter barrel has a lower muzzle velocity and will have less energy to lift the barrel and everyone else agreed among themselves stating that because the 11.5" barrel is shorter and lighter that it would rise more; so which is right? I have searched across the internet when I got home and come to find that there isn't any data surrounding this debate except for other debates on forums and seeing that I do not have my SBR yet, I can't empirically test this either. Even if I did have the SBR available to test against, what tests would verify this for certain?

I decided to approach this problem scientifically, gathering data such as weight of various barrel lengths and the combination of various hand-guards and add that to an averaged weight of the lower, which in this case will be two pounds due to finding data of completed lowers weighing between 1lbs 7oz out to 2+ pounds. As for the weight of the upper, thanks to a post over at 03designgroup.com who collected weight data on various upper configurations, I picked the configurations I have (16") and plan to have (11.5") and used those weights. Now that I have an average weight to work with for sake of comparison, I need to figure out how fast a bullet travels down a barrel between a 16" barrel and a 11.5" barrel. There is fortunately a ton of data regarding muzzle velocities studied by hobbyists, professional hunters/shooters, and bullet manufacturers and that was by far the easiest set of numbers to come across. The data collection reveals these set of numbers to work with;

16" Barrel Upper with 12" Daniel Defense Lite Rail, A2 bird cage

Overall weight (Avg): 5lb 14oz (2.66486 Kg)
Muzzle Velocity (55gr M193 5.56mm NATO): 3132 FPS (954.6336 m/s)

11.5" Barrel with 10" Daniel Defense Lite Rail, A2 bird cage

Overall weight (Avg.): 4lb 14oz (2.21126 Kg)
Muzzle Velocity (55gr M193 5.56mm NATO): 2872 FPS (875.3856000000001 m/s)

Now that we have weight/mass and velocity numbers to work with, we can now figure out the kinetic energy with the formula KE = 1/2MV * V and when we run the above data through we get the kinetic energy (KE) of each barrel configuration as;

16" barrel's KE = 1,214,277.183135022 Joules

11.5" barrel's KE = 847,244.2122672058 Joules

That is a difference of 367,032.9708678162 Joules of kinetic energy produced between the 16" and 11.5" barrel, making a rather significant 69% difference in kinetic energy output between the two barrel lengths which goes to prove my theory of the lower velocities creating less energy to lift the barrel up.

Yay physics and now to go collect on those bets I made, get ready to pay up suckers.