I think there may have been a topic like this before, but oh well.
I refuse to rank Kenji Yamamoto on the grounds that his plagiarism means it isn't his own music, and I refuse to expose myself to it beyond my somewhat vague memories of having watched a bunch of Kai when it was new, and playing a bunch of Budokai 3 when I was a kid, so my familiarity with it is too poor to judge it anyway.
1.
Akihito Tokunaga (1996-1997 - Dragon Ball GT, 10th anniversary movie)
Wonderful in every respect. To be honest, I prefer Tokunaga to Kikuchi.
2.
Ron Wasserman (1996-1997 - Funimation/Saban DBZ dub episodes 1-53, Z movie 3)
An honestly really solid score. It often suffers from the 2edgy4me vibe that permeates many of the dub replacement scores, but as shown by
the first section of this piece of his OST on its own, his score was fully capable of being light and fluffy.
The themes are generally good... It's just a good score. It was wrong for Funi to replace the score and mandate something with a 2edgy4me vibe, but to be honest, this is the one replacement score that did it seriously well.
3.
Anitunes (2001-2003 - Ocean/Westwood DBZ dub episodes 108-276)
Arguably, this should be split into two categories; the score from before and after Ocean commissioned Anitunes to compose some new music for the show in the Boo saga. But, to be honest, even before, when the score was purely tracks Ocean had in their free-to-use library from previous work with Anitunes, the result was a very non-intrusive score lacking the 2edgy4me vibe of most replacement scores. It wasn't overbearing, if anything it was quite atmospheric, with the way it was often played quietly, leaving the actors, SFX, and animation to take the centre stage.
It also helps that several of the tracks are quite catchy, particularly after Anitunes was actually hired to compose some new themes (they will have been sent a few episodes to fully score, then they would have supplied their score for those episodes, as well as each theme used in those, with some variations, for use in the rest of the series), but even before that, the Monster Rancher music that was infused into the show after the Cell Games saga did wonders.
To be honest, I'm a nostalgic fanboy, so the fact I rank this so highly is at least partially due to my love of the Ocean Studios/Westwood Media dub of DBZ, but frankly I do think this score is quite good.
4.
Peter Berring (1995 - Funimation/BLT DB dub episodes 1-13, movie 1)
The closest any of the dub replacement scores get to replicating the feel of the original. Admittedly, it sounds a bit dated now, using some rather cheap, old synthesisers, but it's quite charming, to be frank.
5.
Nathan Johnson (2005-2006 Funimation in-house DBZ dub episodes 1-67, Z movies 2-3, 10, 12-13)
To be honest, it's not hugely memorable, I'm not a fan, it leans way too hard into the 2edgy4me vibe, but I think it just fits the show a bit better than the stuff I've ranked below it, so I really just have to put it here.
6.
Team Faulconer (1999-2003 Funimation in-house DBZ dub episodes 54-276/68-291, Z movie 4)
I don't think Faulconer's music fits the show, I think it sounds cheap as hell, and there are SO MANY boring filler tracks. However, in Team Faulconer's defense, the themes are generally memorable, there are a lot of rather good tracks, and personally, I love this music in the Legacy of Goku 2 & Buu's Fury.
7.
Mark Menza (2003-2005 Funimation in-house GT dub, Z movies 1, 6-9, 11)
Once again, I honestly quite like the music here, and unlike Faulconer, the production is quite good too. Unfortunately, a Dragon Ball score has never been less fitting, and his music is pretty symbolic of everything that was wrong with Funi's version of GT. GT is not a great show, but what Funimation did was akin to turning The Phantom Menace into Attack Of The Clones... They took something that had a legitimate effort and vision behind it, and took out all of its charm, turning it into something completely joyless and devoid of any value whatsoever. Unfortunately, this stains Menza's (honestly rather good) music that he composed for the series, since its presence was used to give the "edgy" vibe that Funimation wanted to put in GT.
But it could be worse...
8.
Nohirito Sumitomo (2014-present Dragon Ball Kai: The Final Chapters, Super, Battle of Gods, Resurrection F, Super Broly)
Oh dear.
I'm sure he's done good work on other things, but not only does his work not fit Dragon Ball even remotely, it's also incredibly bland, bad music for the most part.
The best compliment I can give his work on Dragon Ball is that I didn't notice the music most of the time when I was watching Broly.
I would honestly take Mark Menza's work over this, because at least I would enjoy the music.
The point of Dragon Ball is to enjoy it. Never lose sight of that.