that's a 40% difference. And there may be strength bonuses involved, and aren't they multiplied in PF? (edit: I mean when using a two-handed weapon). I don't think we know enough to make a reliable analysis yet... but one day we will.
So, after this conversation, I threw together a spreadheet to do a more detailed analysis that does take strength mod into account. I had to make a few assumptions (like, for example, that a natural 20 is still a crit even if it isn't 10 above the target number) and I didn't multiply the strength mod for 2-handed weapons, so this probably isn't 100% accurate. It also doesn't take into account things like Power Attack, or other abilities that might add damage on a hit. But it's a start.
The "X to hit" at the top refers to the required number to hit with the first attack. The damage values are cumulative, so for example the 15.4 expected damage from 2 attacks with a 2d6 weapon at 7 to hit includes the 9.9 expected damage from the first attack. I used +4 as the damage mod, since that's what everyone in the video seemed to have in their main stat.
What I'm seeing from this is that with any target number and any number of attacks, a 2-handed weapon puts out the the clear highest DPR, and that's assuming a 2-hander
doesn't multiply the strength mod. If you're not using a 2-hander, then one d8 weapon is usually better than dual-wielding a d8 and a d6 nimble weapon unless you attack three times, though the difference is very small either way. A single d6 nimble weapon is of course always going to have lower raw DPR than a d8 non-nimble, even with three attacks, but it might be worth the trade off if hitting at all is more important than hitting hard, such as if you have something like Sneak Attack or your opponents have very low HP. What is absolutely certain though is
if the defensive value of a shield is worth the damage drop off from a 2d6 2-hander to a 1d8 weapon, then it's absolutely not worth sacrificing that defensive value in favor of the very small damage increase from dual-wielding.
Now, it's probably safe to assume that there will be Feats that make dual-wielding worthwhile for those who want to invest in it (I expect probably some Weapon Proficiency Feats, and some Ranger Class Feats, if nothing else). But for anyone who isn't built for it, dual-wielding is pretty much only going to be useful as a backup for shield users if their shield breaks, or for characters who don't have Proficiency with shields or any decent 2-handers.