That is the highest deductible plan (bronze in Obamacare parlance). Yearly visits are covered, as are milestone visits for children. Other than that we pay out of pocket. Our total amount per year that we are responsible for beyond premiums is capped at $6k per person and $13k for the entire family (I believe; the actual numbers might be a little different, but these are in the ballpark).
My take is that if your family is relatively healthy, then you should go for the lowest tier plan. Then you count on paying the premiums, plus some more for whatever doctor visits normally take place. Then, in the worst case scenario (something expensive happens to 2 family members), you would pay a (roughly) additional 100% of the cost of your premiums in a given year in medical costs. If you have pre-existing conditions or go to the doctor a lot, then a higher tier plan might make more sense for you.
Oh, forgot to mention, $950/mo for our family is the unsubsidized cost. Depending on your family's income, you could qualify for a subsidy from the government, which can be pretty significant. We qualified for a $400/mo subsidy this year (so total monthly cost is $550).
My big picture take on the U.S. vs. the rest of the world is that if you're a high earner, the U.S. is usually better, economically. The pay tends to be way higher here than in Canada or Europe (especially in the tech industry) and a social safety net can be purchased (in addition to health insurance, you can also buy yourself unemployment and life insurance, for example). I've done the math on moving to Canada (my wife is Canadian) and it ain't pretty. It would represent a huge reduction in our effective income.