First, I want to say I am a fan of FuNKyShO's work. I believe his Youtube comparison videos have busted a lot of common misconceptions about IV's, movesets, etc.
Recently, FuNKyShO's research on the subject has made "breakpoint" one of the top trending buzzwords in the PoGo community. This trend has in turn led many trainers to be almost obsessive about attack IV's, to the point where, for example, one poster on this site recently chose to power up something like a 15/12/11 (A/D/S) mon over a 14/14/14 one of the same species, due, presumably to the 15 attack IV. And I believe the mon in question was either a Zapdos or Moltres, which already has attack as its highest base stat.
I was reminded of some of FuNKyShO's earlier work, where he compared high-IV attackers to similar ones with low IV's. Here are the links:
https://www.youtube.com/watch?v=P43Iiu7-PTo
https://www.youtube.com/watch?v=dWsgvMVXr1M
Spoiler alert: the low IV attackers take only about 1-3 seconds longer to defeat the same defender.
In case people prefer Pokebattler simulations over FuNKyShO's excellent vids, I just ran comparison simulations with three different level 30 Dragonites against a perfect 15/15/15 level 30 Snorlax. Dragonite #1 had IV's of 15/15/15 (again, A/D/S); #2 was 0/15/15, and #3 was 0/0/0. The Snorlax had ZH/HS for its moveset, while the Dragonites all had DT/O. Attack strategy was Dodge Specials with Realistic Dodging.
Dragonite #1 defeated the Snorlax in 34.0 sec.
Dragonite #2 defeated the Snorlax in 36.9 sec.
Dragonite #3 defeated the Snorlax in 37.5 sec.
1 lost 96 HP during the battle
2 lost 118 HP during the battle
3 lost 117 HP during the battle
I did a similar comparison using a Blissey as the defender, with similar results, but in the interest of space, I won't post all the details here. Feel free to run your own simulations.
My point/conclusion is that the practical difference between a 0 attack IV and a perfect 15 attack IV was only 3-4 seconds battle time, and that was against tough defenders like Snorlax and Blissey. So, yes, the attack IV and resultant breakpoint do make a difference, but it is a lot smaller than one would think based on the common recent obsession with 15 attack IV's, and it is hard to justify sacrificing several points on the defense & stamina IV's simply to go from a 14 to a 15 on the attack IV.
One more point: I tried one more comparison, changing the Dragonites quick move to DB, since one would expect the breakpoint to matter more with a faster, lower-damage attack. Indeed, the battle time difference is a little greater, but only by about a second.
I hope at least a few people will give this some thought before choosing to power up a 15/11/11 attacker over a similar 14/14/14 one.