I’ve been real interested in researching this and testing what I have available. There isn’t quite 100% confirmed hardtail vs full squish that I’ve seen. I’ve seen a few YouTube tests that all have been debunked in the test methods. Dylan Johnson did some testing that showed there is no effect of a shock lockout, the problem is that the inefficiency of pedal bob essentially happens before the crank, so it doesn’t get measured. 300w at the crank is going to equal 300w minus drivetrain loss at the hub, no matter the suspension type, but the rider may be working harder to produce 300w at the crank. Imagine the pedal stroke being a perfect circle, as in a hardtail or fully locked full squish. If the suspension is bobbing, that now becomes an oval, with the minor diameter equaling the diameter of the hardtail circle (aka crank length times two), and major diameter equaling the minor diameter plus pedal bob. You may be making the same torque at the pedal and the cadence sensor reading the same RPM, but the oval scenario is going to have your feet traveling on a longer path to produce that same power, meaning your body has to exert more energy to make those 300w. The complicated way to say, it is true that pedal bob means your body/feet are moving without all that power going into the pedals, that inefficiency just isn’t captured by the power meter. The hard part is that the rider would need to be instrumented in some way to actually capture this, CO2 rates in breaths, or something like that.
Another aspect is how the tires interact with the road. It’s the same phenomenon as to why lower pressure tires can often be faster (https://silca.cc/blogs/silca/part-4b-rolling-resistance-and-impedance). If the tire pressure is too high, the tire is almost sending high shock waves back at the bike when hitting bumps, slowing it down. Same is true for suspension, hitting braking bumps with a rigid fork/frame really slows the bike down, just from that impact force pushing back through the tires. If you have front/rear suspension, the tires are able to blow-off, letting it float over the bumps. Then with full squish, the pedal stroke is also smoother and easier to put power down as the trail gets more bumpy. There’s a straightaway that’s mildly rooty in which my buddy and I have probably ridden a hundred times between the two of us. We’ve both concluded that not only is the full squish fastest (despite being a few lbs heavier), but can actually put more power down.
So the high level formula would be:
[Power exerted by rider] - [Pedal bob inefficiency] - [Impedance of road surface into bike] = Output
On a perfectly smooth road, impedance will be low and not matter much, so optimizing pedal bob efficiency and weight is most important. As it gets bumpier, impedance goes up, as well as a less efficient pedal stroke. At some point, the full squish will be faster. In my experience, my 25lb full squish is faster on every MTB trail I’ve ridden than my 23 lb hardtail with the same tires, even smoother XC style trails, so even though it’s less “efficient” (as in exerted energy vs power meter reading), the rest of the equation makes up for it and then some. I rode a hardtail this past weekend at a race, because it was 50% gravel and the singletrack is smooth flow trail, only a handful of roots.
In reply to the OP, using the power pedals on both bikes won’t give quite the same results, because of the fact that there’s some power loss pre-pedals. If you average the same power and are faster on the full squish, you may be exerting more energy and not knowing it. Without having expensive laboratory equipment to instrument your body, I think just doing a bunch of laps with each bike will show the true story. At least for me, I do my bike/suspension/tire testing at a local trail that I’ve ridden over 80 times. I have enough lap times that if I know I’m fresh, go when there’s no/low traffic, and really give it a go, that within a few laps I’ll have a pretty good idea whether the new bike/tire/setup is better or worse. Also using Strava’s “compare” feature is great for seeing where each bike is faster.