It depends on the insurance- sometimes you can have a high deductible plus a copay that is a fixed amount (eg. $20 every visit) or coinsurance (eg. 20% of whatever the care costs). A lot of plans will have out of pocket maximums, so you dont ever pay more than $5000 or whatever the limit is. My husband's company recently began offering a health savings account in addition to the traditional insurance option- neither is particularly cheap, so we had to do the math to figure out what would be best for our family. Basically we looked at our bills from the last year and what we paid out of pocket, in premiums, copays, etc. and compared the two insurance structures. Then you have to look at how much you want to risk having to pay if something bad happens or you use more care in a given year than you expect. Insurance is really complicated and I would definitely read the fine print or consult with someone who knows about this stuff.
I have Kaiser in Colorado and have been pretty happy with it. I am insured separate from husband and kids, who dont have Kaiser, because it was cheaper to do it this way. Kaiser is nice in that its sort of a one stop shop- you go to doctor, get your prescriptions, have lab procedures all in one place. Plus they have a great website which helps when making appointments, seeing test results, and you can actually email your doctor. That being said- I have never had a major health issue or hospitalization and have concerns about being limited to their network if such a thing happened. A risk I am willing to take for now.
My husband did have to self-insure for a while and Kaiser was the cheapest option, with a pre-existing condition. he had to demonstrate that his condition is being managed and he is compliant with his treatment. He was initially denied by everywhere he applied to, but Kaiser was reasonable when he fought the denials.