The "cheek weld" did not really resonate with me or help my underlying question, as I was interested in the optical properties of FFP vs SFP. It seems like the FFP should be better than teh SFP, but what proof is there?
This stems from having an apparent problem with more open groups with my Hawke Airmax. I could just not get my groups to "tighten" up (less the 0.75" at 55 yards) that I knew that the rifle could do better on (I had 0.23" at 55 yds before). I could see the pellet just start off-course and wind up as a "flyer" I would agree that inconsistent head position probably was an underlying issue, but with a fixed distance and all the time in the world to get the focus/parallax right - my head position "should" not matter. After all it is hard to be perfectly in the same position every time over 100 shots - I think that is why those old Tyrolean stocks came to be. I even tried drilling a "peep sight" into the fancy metal Hawke scope cap to "restrain" my eye position in the "perfect" spot without much success. One British writer suggested a 8mm peep on the objective end, which I did not try (yet). Well the truth is that the Hawke was just not focusing well enough to set the parallax correctly.
Yesterday with some time and very nice weather, I tried out my 4 best scopes: my replacement Hawke Airmax 4-16x50 (SFP), Athlon Talos 6x24x50 (SFP) against Athlon Talos BTR 4-14x44 (FFP) and Athlon Argos BTR 6-24x50 (FFP). I used the A-Team Parallax Adjustment Procedure and it really helped understand/observe what was going on (link down below). One understanding is that the ocular adjustment adjusts the clarity of the overall picture - both reticle AND object, should be done/fine tuned at the END, and then locked in. Adjusting the ocular lens to a clear sky will not get the full image perfectly/adequately in focus.
Anyway, setting the scopes up on a table and sand bags, I was able with the head bob to get a "perfect" parallax at 10 yards, then adjusted the clarity of the image with the ocular adjustment. I used a excel-style table to look at to see the reticle movement during the head bob, which worked out well. Through this process, the FFP seemed to have just as much movement as a SFP when the parallax is off and you do a head bob. Even, if it was off just a little bit with the FFP or SFP, at 55 yards I was getting 0.5" movement! You could miss a field target with that amount of error. I observed that even with my "peep" sighted scope cap on the Airmax, I could still get movement when the parallax was off (plus it really messed up the clarity).
I did notice that the clarity of the scope was the most important feature. I suspect that this is because - if you can't get a clear image, you probably can't get a good parallax adjustment in the field. Head bob in field target would be very tough, so you have to rely on a clear focused image as the guage. Overall the cheaper Athlon Talos 6x24x50 (SFP) was the absolute clearest scope. Not sure why, but it was the easiest scope to focus properly at 55 yds - which is probably why I recorded such a great 0.23" group with that scope back when I was setting the rifle up. It was even better than the FFP version. The replacement Airmax was the hardest to set properly due to clarity. The Athlon Talos BTR 4-14x44 (FFP) had slack in the parallax knob, so might have to be replaced.
Hopefully that sheds some light - try the A-Team procedure and don't skip steps and I think you will be rewarded.
http://www.bcsportsmen.org/ft/A_Team_Parallax_adjustment_procedure.pdf