While not really "better", 4Kids's openings were, as people say nowadays, "fire" [insert red underlined 100 here].
Aside from them, while not "dubbed", a localized opening that really strikes me as better is the opening for the game Tales of Symphonia: Dawn of the New World/Knight of Ratatosk. Honestly, it's my only experience with the Tales series thus far, aside from buying the steam versions of Zestiria and the original Symphonia, as I received it as a gift when I was younger, so I can't say anything about the other games. Anyway, the original Japanese opening is a happy-sounding J-Pop number, which is good by itself, but just plain
doesn't fit with some of the scenes, in my opinion. The sound briefly changes at moments, but it just seems more like coincidence at times, since the song becomes a tad more subdued before
picking up the tempo while there's a scene of a goddamn town burning, though the tone
does become a bit more "serious".
The orchestral song in the English version may be generic, but it's tailored to fit the animation, whereas the Japanese version, at least to those who don't speak Japanese, seems more along the lines of "dramatic scenes while I play vaguely-fitting music" or something akin to an official AMV.
Not technically an opening, but the 12th English Dub ending of Negima!? (probably at least one of the few anime that aren't dubbed by the 1st company mentioned that doesn't just use the Japanese theme) is a duet by Laura Baily and... Laura Bailey. With fairly distinct character voices for Ayaka Yukihiro and Evangeline A.K. McDowell (whom she voices)! On a certain level, it's certainly a more impressive feat than the Japanese original, which is sung by the 3 voice actresses for Negi Springfield, Asuna Kagurazaka, & Konoka Konoe.