Bullet composition, sectional density, and velocity have more to do with armor penetration than muzzle energy. A vest may stop a 12 gauge slug, but it doesn't mean it will stop a steel core 5.56 with the same energy. It will however still ruin your weekend just due to the impact and crushing damage it does without penetration.
Also, I don't believe a Class III will stop a 30-06 as easily as you think. Perhaps from an angle at range, but point blank at that velocity, I wouldn't be surprised to see it punch right through and stop on the other side. The 110 grain will go through anything short of a Class IV plate for sure. You have a better chance of stopping heavier slower rounds with soft points than lighter, faster rounds, with higher sectional denisity that are constructed to avoid flattening out.
If you want to stop 30 caliber (7.62x25, 7.62x39, 7.62x51, 7.62x54R, 7.62x63, etc...) you need to look beyond Class III and IIIA, and go straight to Class IV.