one question is of course what we see as a significant difference - using the "Rosetta Stone" from https://www.common-cents.info/part3.pdf for your example:
Line No. #5, ERN 5.5, DBI 1685 grains
Line No. #6, ERN 6.5, DBI 1973 grains
the test weight difference is in this case 17% - not really much and I'm sure you won't see a significant difference on video. The stiffness difference needs to be larger, IMHO I'd guess at least 50%. I did once a scatter plot of recommended line weight vs. ERN vs. AA, the overlapping zones are actually quite large:
(the data came from the CCS database)
the question from the OP was
Answering the question is in my opinion actually pretty difficult, because influenced by many variables - for instance "action" of the fly rod depends not just on the stiffness but also on the taper (-> the nonlinearity of the stiffness) and the mass distribution. I've read once from a finish Spey casting guy that they prefer rods with a low AA for long belly spey lines because rods with a tip action or high AA produce more likely tailing loops - so another topic to investigate.Do you believe there is a correlation between the action of the rod and the likelihood of a beginner/intermediate caster throwing tailing loops?
If you want to test the influence of the overall stiffness, you'd have to keep the other variables like taper and weight distribution constant.
Greetings,
Torsten