In your analogy, there's still competition between Linux and Apple. It's not like a designers union passed a law that no more than 3 parameters per app should be available to users.
Within Schengen, there is increasingly competition between governments, too. You can choose anything from a big-government state like Sweden to a small-government state like Latvia, and differences on many other axes as well. Especially true in tech, where things are getting pretty integrated and mobile (and converging on English as the lingua franca).
The problematic part for the big-government states is that there is nothing preventing the Swede from going to government paid school & university in Sweden, making his millions in Latvia and retiring to Spain while still getting his Swedish government pension.
The state pensions these days are tied to where you worked and paid taxes. At least that's the case in Denmark (not as familiar with Sweden). If you work in Denmark 40 years, you're entitled to a full state pension. If you work 20, you're entitled to half of one. If you work 4, you're entitled to 10%. You don't get it solely by citizenship. There is some basic welfare support for those who live in the country, though, e.g. if you're a Danish citizen who lived abroad and ends up back in Denmark dirt poor aged 70 and lacking a pension from elsewhere to support yourself, you won't be on the street. But that is relatively uncommon.
Generally so far it hasn't been a major issue, though things are being continually tweaked, and there are some tax shenanigans especially at the corporate level. But Scandinavia has been fairly successful in the inter-country competition for being seen as a nice place to live. It's pretty uncommon for people who study at university here to pursue careers elsewhere for more than a short period of time, because most Scandinavians prefer to live somewhere with a functioning civil society and government, low levels of crime, good support for raising children, and generally a working social system.
Looking at the direction of net migration, I think Latvia is currently losing that competition: people who attend university in Latvia go to pursue careers in Sweden much more often than the reverse. In fact I would guess that the "low-tax" strategy is partly motivated by an attempt to combat the brain drain. If they weren't losing so badly, they could probably afford to be a higher-tax, higher-service society, but right now they have to compete on price.
