So I’m at a bit of a loss trying to pick a load out between the Laser Cannon and the Rotary Cannon on the AT-RT.

The Laser Cannon is longer range (but can’t be used at range 1) and has Impact 3, but my gut is saying that the extra dice from the Rotary Cannon combined with the surge to crit makes it slightly less effective against an AT-ST but better against any other target.

Has anyone mathed it out to determine which is more effective?

You are correct: on average the Rotary will deal more damage than the Laser against everything except AT-STs and other AT-RTs.

However, Range 4 covers a much larger area than range 1. In the few games I’ve played, Ive found that having laser cannon AT-RTs in the rear rank acting as long range artillary has been very effective. Especially since so far they are the only Rebel units with access to range 4.

It really depends on what else your army has. I'd take a Laser Cannon and a Flamethrower if I'm not taking an ion dude or TF-7. This way I have some form of Impact in my list.

If I'm taking ion dudes, I'd take Rotary Cannons. Now I have more of a generalized force.

As it stands, Laser Cannon deals an average of 2.125 damage with the surge.

Rotary Cannon deals 3.125 with surge.

Against Armor:
Laser Cannon: 2.125
Rotary Cannon: 1.25

The board will also determine how effective each weapon will be. If LOS is blocked, Laser Cannon is severely hampered, but if it's open, Laser Cannon is much better.

For my 3 AT-RT Army, I'm going to take 1 of each to cover my bases.