> The same salary in US could be viewed as 'you are rich' or 'you can't pay rent' depending on with city you live in. Now, you are talking about different continents.
"You can't make rent"/"You can't buy a house with a reasonable commute" an a software dev salary is almost entirely a California and NYC-area phenomenon.
A "typical" software developer (even a junior) could afford a decent house within a reasonable commute in ~7 of the top 10 metro areas in the US (Chicago, Dallas, Houston, Miami, Philadelphia, Atlanta). In the remaining 3 (NYC, LA, DC), you'd probably end up with an unpleasantly long commute, although plenty of people make that choice. If you go further down the list of metros, the ratio is similar.
> How long does it take to buy a house/apartment?
In any of the metro areas mentioned above, you should be able to buy a house on a software dev salary as soon as you've save a 5-10% down payment (so $25-50k for a $500k house, more if you want something bigger/in a nicer area). The difference in salaries vs. Europe would typically allow you to save that within a couple years.
> Can you afford to travel on vacation?
Unambiguous yes - you can afford the monetary cost of a vacation on a software dev salary. Families in much less lucrative fields than software still take vacations.
Paid time off is trickier - European norms are for employers to provide much higher amounts of PTO for all employees, while most American firms are much stingier with it. This is something to explicitly shop around for and use as a decision criteria in a job hunt. There are definitely large American firms that provide 20-25 PTO days standard for new employees.
> Can you save money for your kids' college (or do you even need to do that)?
Annual tuition & mandatory fees at the flagship state university in the median state is ~$12k, so ~$48k for a 4-year degree. This excludes living costs, but you have to pay living costs at European universities as well. If returns on your college investments keep pace with tuition increases (many states have programs that can explicitly guarantee this), then you can pay tuition after 18 years by saving $2700/year per child.
You didn't mention healthcare, which often comes up, but software devs working as full-time employees will typically have good health insurance available through work, so that's not a problem in practice either.
There are tons of reasons to prefer Europe vs. the US (culture, a preference for dense living, lower-pressure work environments, more paid time off, etc.) but overall buying power isn't really one of them. Your salary will buy you more "stuff" (housing, cars, vacations, savings, etc.) in the US, unless you choose to live in one of the highest-cost regions of the country without a correspondingly high salary.