I don't want to debate the semantics of SpS ATM since SpS itself is a fairly large topic of contention due to gains in GCD being difficult to calculate because of the difficulty in simulating fights effectively to understand exactly just what SpS will do for a character. It is certainly something I'd like to revisit later when I get some more time to go through the math.
In terms of stacking Crit, I was curious so here I go. Make any corrections to any errors you find in my logic because I want to be sure I'm accurate for my own curiosity.
This is the absolute highest Crit value a WHM can gain in the current gear tier - a bonus 2,020 Crit for a total of 2,384 critical.
This is table of how stacking a singular stat affects a player's overall effective damage.
+2,020 Crit leads to an effective damage multiplier of 1.138296. Since +0 Crit has a base of 1.02, this leads to an effective increase of 1.138296/1.02 = 11.588%
+2,020 Det leads to an effective damage multiplier of 1.121. Since +0 Det has a base of 1.00, this leads to an effective increase of 12.1%.
Based on the above Crit doesn't actually exceed Determination when super stacking a singular stack. Again, correct me if I'm wrong in my math and/or logic because I want to be sure I'm reading those tables accurately and understand what they represent.
Just to add to Cynfael's comment and ensuring that the information is explicitly clear, this is specific to the Ring slots since you can have two Rings equipped. You can't equip an Augmented Allagan and non-Augmented Allagan piece of equipment in any other slot.
Last thing I want is someone spending their weekly items on slots that can't have both types equipped. ^^;