I'll preface my experiences with all three barrels mentioned in the topic by saying this: I was blessed with the ability to always buy the most broken or F-ed up sample of anything. If there are 10 examples on a shelf with one broken and 9 working... I'll inadvertently pick the broken one 95% of the time.
That being said;
My WOA is an 18" predator model, 1:8 twist. It will not shoot the 77SMK, 77CC, 75 Hornady, 69SMK, or 68 Hornady better than 1.5 MOA, usually much closer to 2 MOA. Powders used were Varget, Reloader 15, CFE-223, and TAC. Primers were CCI 41 and 400. Brass is LC, separated by year. After about 200 rounds of flailing away and trying to figure out (WHAT I) was doing wrong, I was just about to give up when I shot some 55gr Hornady bulk SP with N133 through it...MOA. Holy shit...let's try light bullets and VV powders. I've since found a load for it that uses the Midway 62gr Hornady BTHP with a light load of N135 and will shoot between .3 and .5 MOA. Tried going back to the 68/69gr pills and it turns into a shotgun again. Stocked up on 2,500 bullets and 16lbs of VV powder, so I'm in it for the long haul with my WOA and lighter bullets.
I guess I'm just the one guy who found an extremely picky WOA barrel. At least it shoots well with a couple loads.
My Criterion is on a .308. It is an 18", rifle length gas barrel that had a .068" port. It wouldn't reliably function with anything other than heavy loads, and never locked back on an empty magazine. I had actually posted about it here before. Finally, a well-known gentleman here told me to open the port to .093 and I'd never have that problem again...he was correct. When I contacted Criterion before drilling out the port, they told me .068 was the correct size...call me skeptical. After opening the port that rifle runs like a raped ape.
Anyway, that Criterion barrel is .8 MOA with the first attempt at match ammo, MOA with hunting handloads, MOA with factory Winchester white box 150gr PP, and sub-2 MOA with bulk FMJ. No issues since the port debacle. Won't own another Criterion though.
My Faxon is a pencil barrel .223 on a lightweight build I did for my wife. Other than not knowing I was going to have to thermo fit it to my Aero upper, it has ran fine. I have zero clue about the accuracy though as the rifle wears a red dot...it is as accurate as I can drive a red dot with my astigmatism (2-3 MOA). My experience with this Faxon is the least I have with any barrel.
Also have a Ballistic Advantage SPR. My first one was a dud, but they replaced it. The second one was shooting 62gr M855 way better than I've seen when I was breaking it in. That barrel is with my dad now, so I haven't kept up with it.