The Dragon Ball Super manga's story is based on outlines done by Akira Toriyama, the creator of Dragon Ball, much like the Super anime, and i feel that most of what the anime does, like introducing new transformations, hair colors, change in outfits are mostly done to sell merchandise and evoke nostalgia by coping exact scenes or retreading developments from earlier Dragon Ball series, Toyotaro on the other hand doesn't seem to need to do this kind of thing, going more for the cool factor with break neck speed pacing, but that doesn't always seem work.
The one thing i would say
the anime has over the manga is the comedic filler episodes, mostly from the ones right before the Tournament of Power, with the Baseball, Dr.Slump, Great Saiyaman and Pan/Pilaf episodes being one of the best of the entire Super anime.
I want to start by saying that the Dragon Ball Super manga is automatically better just by rushing through the adaptation of the Battle of Gods arc/movie and entirely skipping that horrible Fukkatsu no F arc/movie.
The art of Toyotaro(aka Toyble, creator of the fan manga Dragon Ball AF) is great, he has some weird construction lines, making a few of the characters look wonky and anatomically incorrect and he likes to reuse shots from the original DB manga and his own shots from Super, but they work for the most part, his main appeal comes from the fact that he apes Toriyama's 80's style mixed with his more recent leaner designs to perfection, and even having some times a more polished work on the fact that he doesn't have the time constraints Toriyama had with the weekly publication at Shonen Jump, plus also having to create the story.
Lots of SPOILERS below
Battle of Gods arc (5.5/10)
Very simple arc, introducing the higher Gods and God Ki.
Much better power scaling than the anime and movie but still weird, making SSJ3Gotenks and Ultimate Gohan irrelevant for some strange reason.
Universe 6 Tournament (5.0/10)
Just a tournament arc put together in a rush, new cool characters in Monaka, Hit, Frost, Cabba, Champa and Vados, plus the God of all things, Zeno, which is way less retarded in this version.
Piccolo and Majin Buu are wasted.
Since there was no Fukkatsu no F arc, there was no teasing of Gohan's comeback and then backing down after just a couple of episodes, the manga gets a pass on this.
Very smart fight on Goku's side against Hit, using the original SSGod transformation, instead of the most useless transformation since SSJ3, the palate swap SSGSSJ or SSJBlue, that was supposed to have perfect ki control, but we learn in this arc that it drains a lot of stamina if used a number of times in a roll, the arc ends with not much happening, and everything goes by too fast, it is a bit of a letdown.
Black/Zamasu arc (5.0/10)
This is where it gets complicated, this arc started great with a lot of promise, the return of Mirai Trunks and a fan fiction level character, Goku Black.
The introduction of Black was great, there is so much suspense and terror in what Trunks was going through, Toyotaro did an awesome job with the reveal of Black being Goku.
This arc was where I started to feel like Super could actually improve, even more so in the manga because it was changing most of what was happening in the anime, taking out stuff like the time travel plot holes, Zamasu’s ridiculous anger towards Goku, Trunks whining on every chance he had, terrible power scaling, SSJ Ikari, plus the episode where Zamasu says that it's Trunks’ fault that he is killing everyone, and even though it doesn’t make sense, the character takes that as a fact and starts moaning again, don’t even start on the Cellphone Mafuba and the Kuwabara Spirit Bomb Sword, none of that was in the manga, thank god.
The manga added a lot of backstory, seeing Trunks training with the Supreme Kai, turning SSJ2 and defeating Dabura and Babidi was great, also we got more great stuff from Gowasu and ‘Shin’ in this version, Merged Zamasu’s great range of techniques, Goku mastering SSB, I even liked Trunks’ role at the end of this arc and the multiplying Zamasus, way better than the anime.
But even though I hold this arc of the manga so much higher than it’s anime counterpart, it still isn’t that great of a story and it leaves so many characters out of it even though it’s supposed to be so grand in scope, and the end even though is better, it’s still the same Deus Ex Machina.
ToP/Preview -- ??
Way more to the point then the anime, making it sometimes feel rushed, but it truly plays out like a battle royale, I don’t know how to feel about it yet.