TL;DR: It's better than the anime, but not by too much. Whatever score you gave the anime, you'll likely find yourself scoring the manga 1 point higher.
This review is written from the perspective of someone who came into this manga after finishing the anime. If you're curious about weather or not to read this, then it depends on what you thought of the anime. If you thought the anime was decent but felt that it tried to be too edgy at times (especially starting from the 2/3rd mark) then you'll find the manga executes the story beats to a much better level than the anime. However, if you didn't enjoy the anime for reasons other than the story trying to be too edgy, then it might be best to give this a skip.
For those of you who are curious about if the anime differed from the manga, then yes it definitely did. however the story beats as a whole is basically the same with minor details being different. Some characters die, others don't, some make different decisions and some don't. That said, a lot of the major story beats are basically the same, the ending is similar (but not the same).
Now for the more in depth review:
The main thing I want to praise the manga is in it's execution. The character were better written, had more impact when things happens to them. This is the most true for the characters on the antagonist's side and is what I would say is the most important strength of the manga. That said, it's not prefect. At it's core, the story of Akame ga Kill is a Shounen series and operates almost entirely within the bounds and established tropes of the genre. That's not to say it doesn't try to differentiate itself from the other series in the genre, it does that plenty. However, for anyone who is familiar with the core tropes and stakes of the genre then there would be very little to be able to catch you by surprise. But even despite this, it manages to execute the tropes of it's genre to a decent level that even if you are fulling expecting everything that will happen, it still manages to leave an impact.
All of this is made possible because of the characters and the setting of the story. The heart of any story is it's characters and Akame ga Kill's manga does much better job of getting you invested in it's characters than the anime and this is why the manga is better executed than the anime as it gets you invested in not only the protagonists but also the antagonists. And this is why the story is able to make it's impact even though the sequence of events follow expectations.
Of course, because this review is written from the perspective of an anime watcher, it would be a crime not to comment on the art of the manga. In simple terms. it's amazing. Nothing short of breathtaking. But because of the inherit stillness of static images, many of the action sequences do feel like something's missing to me. But even despite the limitations of the medium, the art does everything in it's power to convey the motion, speed, ferocity, and power of each explosive fight though the use of it's powerful composition and detailed line work.
And now, we come to the elephant in the room: the edginess. Even if you know nothing about Akame ga Kill, it's likely that you can gather from the title alone that the story is more on the edgy side. And of course, if you've heard anything about the series, you've probably heard something about it's edginess. And if you have already seen the anime, then you know first hand of the series edginess. This is something I cannot deny. However the story uses it's edginess not just as shock value but also to further along it's themes and to tell the story it wants to tell. Are there times that the story is too edgy? yes. But there are also times where the edge is just what the story needed to drive it's emotional peg deep into you making you truly feel the feels. That's the main reason why I find the manga to be better executed than the anime. In the times where the anime gave the feeling of "edgy for edge's sake" the manga is able to make better use of it's characters and the situation to deliver the feels and the edge doesn't feel like it's there for just shock value but rather, it felt like it was there for a reason or as a natural consequence of the events leading up to it.
Finally, we get to the conclusion: should you read the manga and will you enjoy it? My answer to this question is "Probably". What do you look for in a manga? What do you look for in a story? In my opinion, Akame ga Kill executes most aspects of it's narrative to a passing degree. There's nothing about it that I would say is poorly done. That said, i cant say that it excelled in anything other than the art. There's nothing about Akame ga Kill that made made me feel "Wow" there were times where the story made me feel "Ouf". That said, it did have enough of an impact on me that the story is able to make me feel the same way the characters are feeling at times and to me, that's something that I have to give it credit on. At the end of the day, weather you'll enjoy this series or not will entirely depend on if you enjoy the battle shounen genre whole. If you enjoy shounen, you'll definitely find alot of enjoyment in Akame ga Kill. But if it's a genre that you typically avoid, then you probably wont find the series too appealing.