Which critical ring is better for me?

I just go with logic..
I see 3m critical hits and 2.2 normal hits (or 4m and 3.1).
that difference is so big that I don't think even a 40% int ring will get the same effect of having 100% critical.

That's not logic, it's intuition.

If you use the 10% Crit Ring, you gain 7% damage. If you use a 15% INT ring instead and you have less than 214% INT, you gain more than 7% damage, and if you use a 12% INT ring instead and you have less than 171% INT, you gain more than 7% damage. If either of those apply to you, and you still decide to use a 10% crit ring instead of a 12%/15% INT ring, you'll be losing damage.