There are a ton of factors that go into why Europe didn't have a comparable split with the US. There's literally no reason to believe brand loyalty was that reason. It doesn't make sense. Why would Europeans be more brand loyal than the US in general?
Here's one reason: Europe as a whole was not really a console territory until the PlayStation.
Before that gaming was split between consoles, standard Windows PCs, and home computers with proprietary OSes like the Commodore, Spectrum and Amstrad machines. Consoles like the SNES and Mega Drive did fairly well in Europe (though this was still region-specific), but it wasn't until the PlayStation that Europe really bought into a console in huge numbers.
That means that when the PS3 launched in Europe, PlayStation wasn't just the current dominant brand, it also had the nostalgia cachet that something like the NES has in North America. It still has that, plus now another generation of dominance behind it.
That's fine. Are you arguing that they couldn't or wouldn't care about the Xbox brand? That your consumers would buy a Playstation even if it offered an objectively worse experience? Because I don't believe that.
There's limits to brand loyalty. There's hypothetical scenarios where Sony screw up really badly and Microsoft don't and then Europeans swap to Xbox. Stranger things have happened.
However, as
bane833 points out, with the PS3 Sony released a console that was over twice the price of the Xbox 360, they released it almost a year and a half later (after delaying the European release), it was originally a bit of a mess in terms of compatibility and output formats (people who were on forums with lots of European PS3 owners at the time might remember the ridiculous mess of 720p/1080i/1080p options and cable choices and 50Hz/60Hz silliness). The Xbox 360 was simpler, much cheaper, had way more games initially, had a visible performance advantage in multiplayer games, and Sony still won that contest in Europe.
So if all things are equal, Sony will outsell Microsoft in Europe.
If things favour Sony (like this generation), Sony will heavily outsell Microsoft in Europe.
If things favour Microsoft (like last generation), Sony will probably still outsell Microsoft in Europe but Microsoft might catch them in places like the UK.
If that's difficult to imagine then picture Europe as a market where perceptions are half way between North America and Japan. It should be easy enough to accept that unless the console market changes out of all recognition, Microsoft are never ever beating Sony in Japan, right?