Fate/Zero and Psycho-Pass are two good examples where the dub is superior to the subtitled version. They mess up some of the meanings in the subtitled versions, like in Fate/Zero when Saber first appears. In the dub she says “are you worthy, to be my master?” Which is definitely the intended meaning especially once you get further into the show and know how she is, but the subtitles just say “are you my master?” which makes her seem not quite like a dumbass… but it does make you go “wtf kind of question is that?” Not to mention the actual performances. Gilgamesh’s dub voice actor is absolutely perfect for that role, and while the Japanese voice actor is good, he just doesn’t compare.
Similar things with Psycho-Pass. All the meaning gets across pretty well in both version if I remember correctly, but Makashima’s English actor is irreplaceable for that character. His performance alone is worth watching the dub for and it’s just so much better, which is pretty difficult because I watched it subtitled first and I already loved it.
I’m certainly not a subtitle hater though, as everyone knows there are plenty of examples where the dub is terrible in comparison. Then you have shows like My Hero Academia which are interesting, because on the Japanese side they have Tomura Shigaraki who is absolutely perfect for that role. Listening to him in dub is painful to me, as his Japanese voice actor is absolutely perfect in that role. Then on the other hand you have Twice, who isn’t as disappointing to listen to in Japanese as Tomura is in English, but Twice in the English dub is NOT a performance you want to miss out on. It was so annoying watching that show when the two were in scenes together, I’d often switch back and forth between dub and sub just to get the full awesomeness.
All this is to say that it’s really on a case by case basis, and I’d suggest checking out both dub and sub early on (if both are available) that way you don’t get attached to the version you’re used to. Start right and give yourself the best experience from as early on as possible.