Highly debateable. Saint Seiya was huge in other parts of the world, for example. Also, Sailor Moon and Pokemon - both were arguably larger than DB. For me, it was Robotech/Macross.
But yeah, DB (DBZ in particular) was hugely popular in the 90s, with Cartoon Network showing it basically over and over. And remains one of the best of its genre.
I think that's mostly what the GP meant, and I would agree it was quite significant in this regard.
I think DBZ was the first massively popular anime in the western world that leaned heavily into the shonen tropes. Pokemon appealed more to a younger audience, and Sailor Moon was more of a shojo anime.
I remember thinking it was incredibly bizarre at the time, because the delay between the original audio finishing and the reader voice-over made it really hard to hear either audio stream.
growing up in a household that spoke both, it wasn't too hard to pick out both 'streams', and this definitely helped me learn the languages 2x as fast, but it felt like there was more 'processing' going on in my head, and I don't think I enjoyed watching things that way (when later given the choice for one language or the other)
It looks different at first, but I see the same effort to get out of one's sphere and reach for another culture, and start to learn things that aren't in school books, see the world in a different way.
We quickly learned the difference between SECAM and NTSC, how audio was coded on the tapes, why colors were different, the import taxes depending on the price and category, the IP licensing deals, the yen fluctuation etc...while in middle school.
I'd never want to go back, but it sure was a formative journey.
RIP Toriyama
But I think it's fair to say that Dragon Ball was the most ubiquitous piece of anime on the globe across the 90s/2010s and the one with the longest lasting impact
But DBZ (and Sailor Moon) definitely solidified it as a respectable commercial force for the mainstream USA, and gave a unified culture experience that's now pop culture, thanks to millenials getting old.
I also don't know how applicable is making broad statements to europe as a whole in this specific regard. I feel cultural barriers have traditionally been pretty tall and what might be applicable to a country might not be applicable in the same timeframe to a neighboring one.
Then we grow up, manga translations and scanlations became available and we started reading too. That was about around 1990, when Dragon Ball was aired for the first times.
In France, Dragon ball first aired in 1988.
Kids in the 80's didn't say they were watching anime, they said they were watching japanese cartoons. They knew it was different from Disney and Tom&Jerry and other productions but it didn't mean yet what anime meant in the mid 90's with Ghost in the shell, Lodoss and other anime that weren't aired on TVs (and that weren't long running serie).
And then there was someone at FR3 who somehow slipped 3 or 4 hours a harlock captain movies on christma and new year's eve in the beginning of the 90's. That was dope.
In Italy, Dragon Ball was first aired in 1989.
I watched it because it was from the "Dr. Slump guy" that had been aired in 1983, and I had fallen madly in love with it.
I've bought and read both manga later on, in the 90s.
Over the years Dragon Ball has become immensely more popular than Dr. Slump, but I'm fond of the first two chapters (Dragon Ball and Dragon Ball Z), I didn't actually enjoy much anything past Cell.
I like Dragon Ball, but come on, let's be real. You said "the west," but at least in America Dragon Ball (I think only Z aired in America) was extremely niche whereas Pokemon was a widespread cultural phenomenon. Even Digimon was more popular/commercially successful than DBZ in the US.
But since there wasn't many anime shows aired on TV, one had to reach for the internet to get to download other shows. I remember begging my mom for broadband internet rather than dialup, just to be able to download more shows that I would then share with my friends.
Being able to download anime/share translations was definitely a part of the early nerd/internet culture. And DragonBall was the gateway for many to that. RIP Toriyama-san