DR from sources other than a shield/Shield do not keep up with the value from AC bonuses AFAICT. Since putting those up also gives AC, shields/Shields might the better options until spent (though it seems later my suspicions were wrong!).
When facing an enemy within one's normal range (so perhaps not the worst bosses or the pettiest peons), a +1 to attack does about +1/6x damage per attempt (according to math from a Paizo staff member). This doesn't factor in crit effects (like Deadly), carrier effects (like Grab/Constrict or a poison which doesn't double on a crit), or MAP though the 2nd Strike will often fall within the same range too.
So it's spitballing outside the white room.
Inverting this, +1 to AC lowers damage taken by 1/7 and +2 AC by 1/4.
You can compare a normal brute of the level in question to see what 1/7 of their average Strike does (or their Agile Strike for followup attacks).
Then compare that to what DR is available.
So a level 11 Protector's Sphere gives DR 5 (6th level). (It also covers an area so should be better than shield/Shield just for having multiple targets.)
Stone Golem hits for 24 damage, so +1 AC would average at 3.5 less damage taken, but +2 AC would average at 6 less damage.
A Spinosaurus does 27 (+Deadly) so is closer to 4 less and 7 less.
Note that if the dinosaur swallows, the DR becomes more valuable than AC, but then again line of effect is broken if the source comes from outside.
So maybe AC works best when opponents are doing more damage, as in are your level or higher, but DR for when opponents are lower level than you.
Not sure what the equivalent AoE AC boost would be though other than that Bard's Inspire Defense, but that provides DR physical & a bonus to Saves on top, has a much larger area, and can be turned on and off without using Focus Points...so is really awesome. :O
Well, Hymn of Healing at 6th would give Fast Healing 10 and +10 h.p. per round and 20 h.p. per round is darn good. That nullifies most of an at-level hit for one action (after initial two to cast).
But it's only one target and that target needs to get hit every round AND remain injured to benefit so it depends. Place in initiative order matters significantly, especially if there's a healing Cleric trying to assist too.
So +2 AC, to reduce DPR/estimated damage by 20, would need to be facing 80 average incoming damage (not DPR, but average per successful Strike).
A Nalfeshnee (level 14, so +3 as a tough boss), does 33.5 w/ its first Strike and 27.5 w/ its Agile Strike (ignoring that it'd like use other tactics, perhaps because it underestimates piddling heroes or has done its other stuff already).
So that's 61 damage & the +2 AC would reduce the average DPR of that by 15-ish. If it's confidant in its third Strike (like say vs. a guy not in full plate & shield), then the difference rises to 22-ish.
That means the Hymn of Healing is better IF the criteria are met (target gets damaged every round and has an injury to fast heal) and the demon doesn't just swing three times (which a boss might).
If there are other targets, the demon with its genius intellect & wisdom, might switch victims, cast spells (including a Dispel on the Hymn), or Dim Door behind the wall to the squishies and Strike.
Note that a "Level +3" monster's first Strikes might be outside the "normal" range for lower ACs in the party re: the Paizo guy's math estimates. I believe each +1 or -1 has to change both the hit & crit possibilities to fit the estimate. By 11th everybody should be at their class's best AC, but exceptions occur, especially if debuffs and flanking come into play.
I did make a booboo.
Hymn of Healing at 6th heals is FH 12 & +12 h.p., so whether the monster uses its third Strike matters less (though the target being injured and losing those temp h.p. each round still matters a lot).
ETA: And you're welcome. :)