Is a PhD degree from a European university considered equally valuable as one from the US?
One simple answer is no, the two aren't equally valued, because the two are also not even regarded as equal.  As a trite example, consider that many European countries (especially the German-influenced ones) are very picky about which letters you can put before or after your name.  I have a dual-degree, so I am "allowed" to use Dr. as a legal part of my name in Germany; but my officemate with a solely American Ph.D. cannot.  The way in which doctorates are made is also vastly different-- the U.S. requires coursework and then research, (often) mixed with lots of (often underpaid) teaching duties, while European doctorates typically frontload on the research and are light on teaching responsibilities.  Those different experiences produce different palettes of qualificiations and skill sets.  It's no wonder that if you're primarily paid to do research, you'll probably produce a better thesis than someone who had to perform teaching duties 20 hours a week.

However, there's also the danger of regarding "Europe" as a monolith.  I've heard anecdotes from some Italians who struggled to get funding to finish their degrees without taking on big teaching duties. (But see comments by @MassimoOrtolano.)  Croatia, Romania, and Bulgaria all suffer from "brain-drain" as young folk go west for education.  And I get the sense that when people say "Europe" in the context of academia, they're almost always, knowingly or unknowingly, referring to Germany, France, and the UK.  Few other European entities have as much economic, political, or historical influence as those three.

Along the same lines, Europe comprises dozens of different languages and cultures.  Asian students are more likely to already know English than French or German (or Dutch or Polish or Finnish...) and therefore will seek a degree in an English-speaking country.  American culture and accents are more familiar to the world than, say, British or Australian, because of the movie and music industries.  (The UK is also not super stable in terms of immigration standards at the moment.)  Seeking a degree in the U.S. is then just plain easier-- you don't have to spend time learning a new language or adjusting to a new culture.  For these students, it may be that because English is the de facto language of science, the notion of what's considered "prestigious" just followed blindly.