I went through this only recently, so do not know for sure if it would save me money or end up costing more.
My last employer was paying about $1.7K per month for a family of three. Costlier than usual because it was a very good plan. I could not find a with similar levels of coverage and deductibles for cheaper outside.
The key thing that varies between plans (I am based in California) include deductible and coinsurance, which can be traded off with monthly premiums. Lower the former two, the higher the premium.
I pulled out my families older insurance claims data when my employer was paying to estimate my future expenses for each family member. Based on that, I considered various plans and ended up choosing a plan with higher deductibles but lower monthly premium (~$600 for the family). Mostly likely, this will save me a lot over the low deductible plans. This is true even when I expect to be paying just about as much in deductibles/coinsurance per month on an average based on the past data. If things go wrong, I may end up paying a lot more, but still capped by the out-of-pocket maximum that is not much higher than $1.7K per month.