Here are the official specs:

Regulator
Overall Length: 13"
Blade Length: 7 1/2"
Blade Thickness: .333" (Over 5/16")
Handle: Resiprene C
Steel: SR-101
Hardness: Differentially Treated: Spring Tempered body with 59-61 Rc edge.
Weight: 14 1/2 ounces!!!


Son of Dogfather
Steel: SR-77
Hardness: 58 - 60 Rc
Handle: Resiprene C
Thickness: .250"
Blade Length: 7 1/2"
Overall Length: 12 1/2"

So they have the same blade length, but the SOD handle is slightly shorter. The width of the regulator, however, is smaller than that on the SOD, so that might explain why it "looked" smaller. It also has a more aggressively tapered point, which could further contribute to the slimmer look, despite its 1/3 of an inch thickness.