12-ga kicks harder than 10-ga!
Reading the anecdotes, this post's replies got me thinking: Why would anyone really want a 10-ga recoil generator? There aren't many 10-ga slug, upland, nor target loads on the market. The answer is simple, a water-fowler wants a 10-ga for steel shot. Because steel is less dense than lead, more volume is needed, and a steel 10-ga replaces a lead 12-ga.
Might a 3" 12-ga shooting lead kick more than 3-1/2" 10-ga shooting steel?
I looked at Browning BPSs (selected by the OP) and the 10-ga is 2-1/4 pounds, or 27%, heaver than the 12-ga model.
Let's look at steel and lead 1-3/4 oz loads (NS10M & PHV12M by Remington) with payloads similar to the slug shown by the OP:
The 10-ga 3-1/2" waterfowl steel load Nitro Steel High Velocity has a muzzle velocity of 1260 fps, and a similar 12-ga 3" turkey load (plated lead) Premier High Velocity Mag is up a little at 1300 fps.
You can run the numbers, if you want (the difference of the squares of the velocities is 6.4%), won't the 27% heavier 10-ga have significantly less felt recoil (kick) than the similarly loaded 12-ga?
Some food for thought,
Pete