I have only ever had one barrel I could not get to shoot accurately, but it was a first attempt by a fellow at making 'Hand Made' barrels. Apparently, later barrels he hand made shot very well, many exceptionally well.
I watched my brother put 5 consectutive offhand shots at 100 meters, into a group the size of a fine china tea cup, late 1980's I think it was, - yes - 3" for 5 shots offhand at 100 meters with a flintlock rifle with open sights - WE are lucky he can't see well enough or hold well enough to do that today. That is/was an exceptional group, but I was there, I witnessed it. The barrel was a Tonges barrel- with exceptionally deep grooves - .025" or so & a .50 cal. seems to me.
I would add Green Mountain to the "Exceptionally Accurate" barrel list.
Too - my Goodoien .40 was also a peach - advertised as a Match-grade barrel. A friend needed an accurate rifle, so I sold it to him - of course, now I have to compete against him.
My Bill Large .50 barrel from the 70's could easily have been marked as match-grade, although it was a .58, and exceptionally accurate for the day but my GRRW .69 is also "match grade", just a bit harder to shoot accurately due to it's appetite for huge powder charges to give that accuracy with it's 480grou round ball.
I have just ordered a new Rice .32 barrel to replace the barrel currently on my squirrel rifle. I expect the Rice barrel to show much better accuracy than the Whatever-it-is barrel currently on that rifle. The best I can ge with it, is 1" to 2" at 50yards from a rest - obviously THAT one needs to be replaced - it too inaccurate - for me, but I do not know that barrel's make - it's rifling-style of wide lands and narrow grooves matches nothing made in the last 30 years that I've seen.
For killing squirrels at 25 yards, it is all that is needed - it just isn't accurate enough for trail walks where shots run from 12yard card cuts to 120yards steel plates.
So - like the 'boys' (other old guys) asked, what is your required accuracy level and/or type of shooting?
An accurate barrel for trail walks will be quite different from a dedicated match barrel for bench-rest shooting, or different again for a chunk match, or plank shoot- or hunting moose or elk? The trend towards increased capability to produce better accuracy, rises with bore size- but, there comes a trade-off with the increased recoil generated by loads required to produce the accuracy the larger bores are capable of giving you. For example, my .69 is capable of producing exceptional accuracy at 100 to 200 yards, but it requires 165gr. of 2f powder to do it. Slightly less accuracy can be readily obtained with a .58 or .62 using a mere 130 to 140gr. of powder but shooting much lighter balls which have the tendency to kick less, much depending on the style of rifle used.
So - what are your requirements? All of the listed barrel makers can produce accurate barrels - however there are other companies specializing in match-grade barrels for special purposes.