Well... if you change all the variables, then anything goes.
"I wonder what the difference would be if the 243 was using 55 grain bullets and the 22/250 was shooting 80 grain bullets ???????"
How about if the 243 was shooting 105 bullets and the 22-250 was shooting 40 grain bullets... how about if the 243 was a 6# mountain rifle and the 22-250 was a 15# PD rifle, or how about if the 243 was a 15# PD rifle, and the 22-250 was a 6# coyote callin' rifle...
Changing the variable,rifle weight, bullet weight, velocity, powder charge) does change everything, as Catshooter notes.
Luckily it's easy to make an actual calculation mathematically. The FREE Point Blank software includes recoil calculator among its many features. First, with QuickLoad we can get a good estimate of a "practical max load" and the bullet velocity, for each of the "scenario". Then we plug the load numbers into Point Blank. The results are below:
.243 Win at 60,000 PSI Max--
243 shooting 55gr bullets,3920 fps, 45.5 grains of powder) 6-lb rifle: 9.74 ft/lbs recoil energy
243 shooting 55gr bullets,3920 fps, 45.5 grains of powder) 15-lb rifle: 3.90 ft/lbs recoil energy
243 shooting 105gr bullets,3120 fps, 46.5 grains of powder) 6-lb rifle: 15.75 ft/lbs recoil energy
243 shooting 105gr bullets,3120 fps, 46.5 grains of powder) 15-lb rifle: 6.20 ft/lbs recoil energy
22-250 Win at 60,000 PSI--
22-250 shooting 40gr bullets,4250 fps, 38.5 grains of powder) 6-lb rifle: 6.51 ft/lbs recoil energy
22-250 shooting 40gr bullets,4250 fps, 38.5 grains of powder) 15-lb rifle: 2.60 ft/lbs recoil energy
22-250 shooting 80gr bullets,3300 fps, 37.5 grains of powder) 6-lb rifle: 10.24 ft/lbs recoil energy
22-250 shooting 80gr bullets,3300 fps, 37.5 grains of powder) 15-lb rifle: 4.09 ft/lbs recoil energy
NOTE: These numbers aren't absolute--you can juggle the powder options to go somewhat faster or slower or use more/less powder, but this gives you a general idea. Also note, the SAAMI Max for 22-250 is listed at 65,000 psi, but most 22-250 brass won't take that repeatedly, so I used the 60,000 psi number.
Click here to download PointBlank Software:
http://www.huntingnut.com/files/pointblank/PointBlankCRBSv18a.zip