Yes, that's a lot of assumptions. I would think a heavier lens would shake less while hand holding. Physics doesn't lie:
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If you think this, you've never handheld the two lenses in question, or done a comparison between a "big and heavy" lens and a "small and light" lens.
It isn't the lens that is shaking, it's the human that is shaking, and there's much more involved than a drastic oversimplification of mass vs acceleration.
If you have access to any of these lenses - go outside and do some testing. 600TC vs 600PF for example when shooting screech owls, I can consistently get sharp images at 1/6s handheld with the 600PF, but rarely get sharp images at 1/50 or slower with the 600TC. With a 600 F4E FL, that number would probably be 1/100 or faster.
Wotan is correct - the 600 F4E will have better subject isolation due to the shallower DOF, but a lot of commenters point at f6.3 lenses and say it must result in higher ISO, which isn't always true due to the differences in size and weight.
Rich was taking a bit more liberties with his assumptions, I meant shooting both wide open. so 600 F4E at f4 vs 600PF at 6.3. all else equal, you will be able to get the same level of sharpness at a lower ISO with the 600PF when handholding, despite the 1.33 stop loss in aperture.
Of course, if you shoot from a tripod - it matters much less and a monopod makes the difference between the two less than handholding, but not as drastic as the tripod.
and as for your "physics" comment and image taken out of context, look at examples of the affects of weight the further it is from your body. with a small, light lens you can keep it neatly up against you. with one of the big beasts, the center of gravity is further away, which induces more strain and shake.
it's why anyone can hold a mallet close to them without difficulty, but powerlifters challenge themselves to hold the same weight with their arms fully extended - and it's much more difficult.
torque is proportional to the distance from the weight to the point of suspension, your body. more force --> more ATP required --> more tiring -> more shaking
there are also many other factors that would make handholding the F4E more difficult. the existence of a larger hood which acts as a sail, the lesser VR/IS whatever, the older technology which means that lens is not built to be as well balanced as a 600PF/600TC, etc.