Let's recap how apocalyptic overture works. It costs 30 mana, has 2 round lag and there are three "tiers" of the song
1/ fiery/icy illusion - weakest damage, significantly lower than vibrato
2/ fiery/icy ball of fire/icy - mid-range damage, should be better than vibrato but not by much
3/ fiery/icy doom - highest damage, always better than vibrato
I don't know what % chance there is to trigger a tier. (I don't know if it's 1/3rd for each or something else.) My empirical evidence shows that you get either 1/ or 3/. 2/ happens rarer.
There is definitely one edge to improve apocalyptic overture - insinuative overture - but it does NOT improve damage. Rather if your target is resistant to fire/ice, insinuative overture triggers triggers the "other" element. Meaning, if your target is resistant to fire, you are more likely to sing "icy" overture.
Also, there are *rumors* that apocalyptic overture tiers are based on luck. So it's possible that lucky edge will help. (I am personally a bit skeptical.)
Let's recap how vibrato works. It costs 40 mana, has 2 round lag and only has one "tier". It also has a potential to lag the opponent (which potential becomes quite consistent in epic repertoire).
So looking at the two recaps, even just from the damage perspective, vibrato is better for PK situations. It's consistent/reliable damage, not dependent on luck. (In other words, if you did 100 vibratos vs. 100 overtures, I would think overture would win but not by a large margin.) Once you throw in lag on the opponent from vibrato, vibrato wins out by a large margin.