Good discussion
@Todday
It's a good point about tracking barbell jumps of squat jumps. With jump squats I can fairly easily tell if I have improved by the ease at which I amortize in the 1/2 squat position. Videos also help. With the barbell jumps daniel demonstrates, I agree though it is not easy to track improvement. But with power cleans and snatches, it's also tricky, you can flex at the hip more and go deeper into a squat in order to hit a new PR for instance, this is analogous to jumping lower in a jump squat and calling it a PR.
@steven-miller
The abstract was vague indeed. But it had to be because to explain their results would have taken up a few extra sentences. Although the authors are not concerned with what we are concerned with, you can interpret the study differently than they do, and conclude the jump squats result in more power output than the power cleans do.
A note on the isolated body power: the reason it was triple with the unweighted jumps is because they looked at the sacrum, obviously the sacrum will have the highest velocity during a jump with no external resistance. It's not to conclude that body weight jumps are the best way to go I agree. But it does tell us that heavy squats do are not a power exercise, but one to improve force production. If you only perform squats in your jump training you won't optimize your success.
If we lok at just bar power though, the jump squat peak bar power occurred at 80%1RM, with 2527W, and 2145W at 90%1RM in the power clean. So not as much of a difference there.
The other study I referenced found similar values in power output int he jump squat and hang clean, slightly higher in the jump squat. Still measuring power output does not tell us everything. The EMG studies would. I would suspect that jump squats would have more quad involvment.