Of course, the salaries you're talking about here are gross (as in pre-tax), so obviously first step would be to calculate net salary. In US you have to components of the income tax, first the federal tax, then in some cases state tax (California is one of these states, and actually has the highest state tax of all). BTW. what's generally called income tax in Europe, in US goes by name of "payroll tax". Example of tax table and calculator.
You can get rough idea how far given amount of net salary will get you on sites such as Numbeo or Expatistan, which compare cities on cost on living index. Both sites offer option to directly compare two cities in details. Neither gives you complete view, and should be taken with a grain of salt, as it's based on basket of goods and services which don't necessarily reflect your spending. According to cost of living in SF rough similar to Paris — actually SF is 3%-4% cheaper according to comparison by Expatistan and Numbeo. Note, that in this case it really depends on your rent vs. other spending ratio.
In Europe you're usually under some public healthcare plan, in case of US it's private insurance, so that's something that you have to take in account. But in case of Software Engineering jobs you're probably in luck and employer most likely provides that for you, maybe even (at least partially) for your whole family.
As far as days off go, in Europe you have your vacation days, depending on country and your work experience that's anywhere between 18 to 30 days and it's usually regulated by law. You have also right to sick leave that is completely independent of your vacation days. It's not unusually to be whole month off in the summer. On the other hand in most companies in US they have single concept called PTOs (payed days off), which are both vacation and sick days. It probably depends on company culture, but typically you're not expected to use all PTOs (contrary to Europe, where you're expected and even obliged to use all your vacation days). It's also not very typical to have very long vacations.
Retirement founds in US are private, there is 401(k) scheme which makes that tax deferred (i.e. you pay tax on your pension while receiving it, not while investing). IMO for any highly skilled worker with reasonably high salary is actually a good thing compared to European public retirement systems, as in public retirement systems ROI is absolutely terrible, few times less than the worst of private funds.
As far as public transport, don't know about NYC, but SF and whole Bay Area has excellent system with Caltrain, BART, metro, trams and buses. I find it to be relatively inexpensive comparing to for example Amsterdam. For example single bus fare is $2 in SF, €2.80 ($3.90) in Amsterdam, SF Muni & BART monthly pass is $76, roughly equivalent 3-zone Amsterdam GVB monthly pass is €119.50 ($167).