James, you will experience approximately 20 to 26% less recoil with the 20ga yet still have approx. 95% the capability overall of the 12ga. Coach. Where the 12ga will shine slightly better is at extended ranges. The 20ga is a great compromise gauge in my opinion. Lower recoil similar performance. Reminds me of the 308 vs 30.06 comparison.

and if the weight difference of the shotgun is enough it can also recoil more the action type can have a large bearing on it as well a Gas operated semi auto will recoil more than a pump for the lowest recoiling shotgun a remington 1100 12 ga with the 7/8 oz is very easy on the sholder

Shotguns are scaled to gauge(meaning all are proportionately the same size) . Recoil will be different comparing apples to oranges when it comes to shot or slug weight between the two. When comparing apples to apples with shot weight, the same velocity times the lower payload weight of the 20ga will be mathematically less according to the laws of physics. I would personally get the 12 for load versatility (low recoil/low dram) loads. (I do agree with Randy that if the payload weight is the same, the lighter 20ga can recoil more). huntinggearguy.com/shotgun-reviews/12-gauge-vs-20-gauge/

to continue here is a real low recoil 12 ga round this would have less recoil in a 12 ga gun (heavier) than a 7/8 oz round in a 20 ga gun of the same type
Federal Top Gun Extra Lite Ammunition 12 Gauge 2-3/4" 7/8 oz #8 Shot This load is a great choice for the shooter looking for target ammunition to hit the clay fields. The extra-lite load is loaded with a special powder from Alliant to help make it a manageable, soft kicking target load.Caliber 12 Gauge
Quantity Please select
Shell Length 2-3/4"
Shot or Slug Type Lead Shot
Shot Size #8
NonToxic No
Buffered No
Muzzle Velocity 1200 Feet Per Second
Primer Boxer
Corrosive No
Reloadable Yes
Barrel Type Smooth Bore
Shot Weight 7/8 Ounce
Crimp 8-Point Star
Dram Equivalent 2-3/4
Country of Origin United States of America

recoil is a very subjective thing sometimes 20 ga guns can have more recoil than 12 ga gun depending on the weight of the gun and the shell used a heavier 12 ga gun shooting 1 oz (standard is 1 1/8 oz but 1 oz is also common) loads will recoil about the same as a 1lb lighter 20 ga with 7/8 oz loads (standard load but 1 oz loads are available in 20 ga also) now if you shot a 1oz 20 ga load in the same lighter gun it would be a kicker. if you hunt around you can find low recoil 7/8 oz 12 ga loads will is what we use along with a 12 ga auto loader teaching skeet to kids because it is about as low recoil as shotguns in guns that thekids can hit targets with .410 is to hard to hit targets with for the kids