Well, my assumption that the two hammers were accelerating at the same rate was incorrect. When I'm wrong, I'm wrong -- or at least, somewhat inaccurate.
I did a slo-mo video of hitting with both the treadle and hand hammers, going more or less all-out with both. The quality isn't good enough to post, but a few takes-away:
The hand hammer does travel faster than the treadle, taking about 3/4 of the time to cover the distance from the top to the bottom of the blow.
In that time, the hammer covers a slightly longer distance, as the top of its arc is slightly higher than the uppermost position of the treadle hammer.
Therefore, the hand hammer is accelerating faster than the treadle hammer. (N.B.: I haven't done precise measurements or calculations, but I'm going to guess that the ratio of hand hammer to treadle hammer acceleration is somewhere between 1:6 and 1:8.)
It's worth noting that the range of motion on the treadle and the linkage does not bring the hammer all the way down to the anvil. The reasons for this are complicated, but this means that at the bottom of the stroke, the hammer is carried forward by its own inertia and is to a small extent fighting against the tension on the return springs, which may diminish the snap slightly. However, this is less of a problem when you're hitting a top tool, as the point of impact is higher above the anvil than when you're just hitting a 2x4.
Recovery time between blows is shorter with a hand hammer than with the treadle hammer.
In sum, the treadle hammer hits harder but slower; the hand hammer hits lighter, but faster. More modifications to be made, more video to be shot, more calculations to figure....