I will list just the ones I know:
1. Shunsuke Kikuchi (DB, Original Z, 2008 OVA, and 1-98 replacement)
2. Norihito Sumitomo (BoG, Kai 99-167, RoF, Super and DBSBroly)
3. Hiroshi Takaki (Ultimate Blast, Gaiden Remake and Ep of Bardock)
4. Kenji Yamamoto (Some games and Kai episodes 1-95 before the replacement)
5. Yuya Moori (Super Dragon Ball Heroes anime)
6. Akihito Tokunaga (GT)
7. Bruce Faulconer (Z)
1.The Master of DB musics,
Master Kikuchi always will be my favorite, his soundtracks with a lot of drums bass similar to the classics military armys musics, his trumpets are the main element in his music and is unique! and fits totally with the old style of the series! specially with the martial arts style of DB Classic, he was the first one and probably the one who had composed the biggest number of musics, being them more than 500 musics, I just hate that a big part of the soundtracks are so damn short, but was Toei's fault why everyone prefer Yamamoto or had hated Kikuchi's replacement in Kai, because they've chosed just a few variated tracks and most of them were overused and unfitting! after that I think Kikuchi didn't even wanted to see Toei's face anymore! what a underrated composer!
, Sumitomo is pretty of other underrated guy too, everyone says he's mediocre or bad, but for me he's the modern Kikuchi, obviously don't even is near to Kikuchi, but his soundtracks specially in Battle of Gods opened the new generation of musics, the way how today now is everything eletronic, digital and new, I think his soundtrack is a very good example, Kikuchi was perfect for the past when everything was hand-draw and old school feeling, in my opinion Battle of Gods was the best he could do, "Life to Be Protected" is my favorite Sumitomo music, along with "Eternal Universe Brand New Friendship" being my favorite of his sad/melancholic themes, RoF wans't very surprising but was awesome too, the track used for when Goku defeats Freeza is my favorite of his various themes with vocals, in Super, his first works really were pretty mediocre, but was increased at Universe 6 Tournament arc, his classic "The Final Death Match" got famous WorldWide! and "Fierce Battle Against a Mighty Foe" & "The Power to Resist" are my favorite battle themes, now I think his work in Kai 2014 was his worst work, like is prety good some tracks, obviously has some awesome tracks like the for some reason unreleased track "No More" or know as "Vegetto vs Zamasu", and the track used for when all the Universes are restored in Super 131 as well, but a big part are just boring repetitive themes, I don't like this track (https://www.youtube.com/watch?v=KgSgHXmOwNA
) in both Kai 2014 and Super this track was overused as hell, just had noticed most of the released musics are bad and the unreleased ones are good. I would prefer if Toei had reused Kikuchi soundtracks in the new Broly movie, but I'm happy that Sumitomo is still there, 3 tracks were already revealed.
3.The Ignored One
Hiroshi Takaki is obviously not famous, but he's one of my favorites, I'm not a big fan of his Ultimate Blast musics, since because they all are just rock, but I loved his work in Episode of Bardock the 2010 Remake of Gaiden, so bad none of his soundtracks for the two OVAS were ever released :\
4.Plagiarism but can't be Forgotten
The Good Old Yamamoto, I so bad for what was happened with him, I need to admit that I just had heard a small percentage of his soundtracks, but just with this I think he's good even with the plagiarism, I enjoyed his soundtracks for the Budokai series, fits very well with the style of the games, now his work in Kai, well for me is good but I don't think it fits perfectly with Dragon Ball, but it's fun to watch Kai with his score, like, here in Brazil, just the Kikuchi version of Kai 1-98 was dubbed, and even Kikuchi being my favorite, because of Toei's horrendous Kikuchi's BGM edit in Kai, I would prefer to watch the Yamamoto version.
5.Mini fusion of the Three above
Yuya Moori, he's definitely new yet, he made the soundtrack for the promotional anime of SDBH, maybe he will do for SDBH World Mission, well in my opinion his tracks are a fusion of Yamamoto, Takaki and Sumitomo, so why I listed him as 5? well because his tracks for me aren't very variated, all of them are just a lot of intense music with bass, the calm tracks are literally the same thing, it's a good compositor too but he should increase his work a bit.
6.Tried to surpass Kikuchi
Tokunaga was hired to take place of Kikuchi after he was retired when Z was ended, working for GT, I believe that me and everyone can enjoy his soundtracks, just as Kikuchi did, creating instrumental variations of Makafushigi Adventure, Chala and Angels, Tokunaga did variations of Dan Dan, the problem is that his variations are the same thing, Kikuchi variations are happy, calm, agitated and intense, Kotunaga Dan Dan variations are just calm and melancholic without much difference, now the rest of his soundtracks aren't memorable and addictable, much of them are the same with that 70's quality, I think the melancholic tracks are the best, now the entire I think fits better with those 70's animes with Giant Robot or about spaces, not with Dragon Ball.
7.Good, but not Dragon Ball
The Our Boy Bruce Faulconer,definitely the most famous composer (or composers, idk), Yeah I understand, the musics are awesome, but in opinion don't works with Dragon Ball, just a bunch of rock musics, let's take M1109 and the SSJ3 Theme, the SSJ3 Theme from Faulconer, just gives you the feelings of "wow, so cool and badass!", but I'm really sure that's not the reaction Toei (or Akira, idk) wanted from the people who had watched the scene, SSJ3 theme is just too calm and don't makes it like that is the end of the world, now M1109 from Kikuchi, is perfect, the track begins from a intense bass to a calm part, but the calm part also gives the feelings of "aaaa what is happening, this don't looks good", and later backs to the intense part, and now it gives the feeling of "aaaa is the end of the world!!", gives totally the sentiment of that is the apocalipse, something dangerous, scary, and yeah, legendary! and I really sure that's what they wanted as the reaction of who had watched the scene, I never cared or was a fan of Faulconer, people say it's perfect, but for me it really don't works for dragon ball, try to compare the Gogeta's born scene, the Faulconer music used just makes the fusion look cool or badass, now M2024 from Kikuchi makes the fusion legendary!
I never heard about Johnson, Wasserman or Menza, so I don't even say something about them here, lol I never knew that GT's soundtrack was replaced too in Funi!