I'd like to preface this review with the fact that I LOVE this series. I'm probably biased because it hits me right in all of the different features that I enjoy in manga. I only read it in the last few days, and it was a complete binge because I couldn't put it down. I've been reading manga for most of my life, and I think the only one I've enjoyed more was Shaman King, but this series has a long way to go, and may prove to be my favorite. I absolutely can't wait until it's licensed to be released in English.
Gushing aside, as of the time of this writing, only up to chapter 31 has been translated (even by fans, as far as I can find), so that's what I'm going on. The anime looked good, so I picked it up, only to not want to wait for the next episode to come out. So I decided to read the manga. It's just as good as the anime, if not better.
The story is handled very well. There are three factions fighting towards an end goal and against each other. Things are very clear when it comes to figuring out where the story is going--and yet not completely predictable. It's very much a common setup for the target audience genre, but that's certainly not a bad thing.
The art is extremely clear and nice to look at. The artist does a very good job with not only scenery and characters, but action scenes as well. It's all framed in a very nice way and it's easy to tell when you're looking at a comedic scene and when you're looking at a serious scene.
The characters are great, and with time, they're being fleshed out more. At this time, I think it's best to leave this category at "they have a lot of promise and the series hints that the promise will come to fruition."
I'm obviously enjoying this manga a lot, since I binged it and then scoured the internet for more translations once I was caught up.
Overall, I'd definitely suggest this to anyone and everyone--and I have been. Bungou Stray Dogs is a great read and it's looking like that will be the case for quite a while to come.