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Muzzle energy and recoil energy can NOT possibly be the same. This is not a case of conservation of energy, but conservation of momentum.
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This is where things get confusing, for me, at least. Different math formulas, different terms for energy measurement at different places, etc.
Physics is a fantastic thing, but there are places in physics where the math works but reality doesn't. Friend was working a physics problem once, I was a little interested, but amazed about the "conclusion".
the situation was, a swimmer starts at one end of a pool, swims to the other end, and then returns, getting out exactly where they got in. Now, here's what amazed me, what the book wanted the student to do was show the work (formulas and calculations) that proved that the swimmer went nowhere.
To me, the swimmer went down, and back so they went somewhere, despite getting out right where they got it, but the "physics" formulas said the swimmer went "nowhere" and they wanted the student to show the proof of that.
SO, no matter what formulas you use, where you measure, and what you call it, since ALL the energy in the system comes from the firing of the round, how can recoil energy and muzzle energy NOT be exactly the same???
OK, I get how the different masses of bullet, gun, shooter, powder gas, everything involved is a factor, and these change the numbers when measured at different points in the system (and different points in time) but since all the energy comes from the round to begin with how can it not be the same, just looking different due to different to the numbers and formulas used expressing it??
Are we in a situation like the old story. where engineers calculate the bumble bee cannot fly, but the bee, does not know this, and flys anyway?
You can calculate which load will, on paper, have less recoil in your gun. BUT, what you feel is what you feel, and its not impossible that what looks like a significant difference on paper might not be as big a felt difference, in your hands.