SMN BIS 2.3

[pacifist0rz]

Note that for this post I will be using the coefficients from http://ffxiv.ariyala.com (even though my testing has shown that crit should be weighted higher than this)
WP = 6.57
Int = 1
Crit = 0.211
Det = 0.283
SS = 0.094

Judgment ring of casting should be better than High Allagan Ring, Has 17 crit and 9 det
http://xivdb.com/?item/8354/Judgment-Ring-of-Casting
As long as you meet the acc req in coil.

This statement is totally correct.

2 int + 13 spell SS from HA = 3.2
17 crit + 9 det from Judgement ring = 6.1 (+2.9)

However now we need to focus on that last sentence "As long as you meet the acc req in coil." Any BIS build will be hovering right around the Acc cap, so we still need to figure out a way to make up the lost Acc from the HA ring.
Lets look at some possibilities...

Earrings (swap HA with Sold):
HA = 19 crit + 9 det = 6.6
Sold = 13 det = 3.7 (-2.9)

Boots (swap Sold with HA):
Sold = 25 crit + 18 SS = 7.0
HA = 18 crit = 3.8 (-3.2)

Wrist (swap Sold with HA):
Sold = 13 crit + 13 det = 6.4
HA = 13 crit = 2.7 (-3.7)

As you can see, any swap that you make will cancel out the gains from the judgement ring, with the boots or wrist swap actual being worse. Also not for someone like me who values crit more than http://ffxiv.ariyala.com, even the earring swap is worse.