Both animes are centralized around a tight-nit group of supernatural (and kick ass) individuals who all seem to be haunted by their pasts in some way. The same type of light comedy is scattered throughout and the characters are lovable and interesting. The same thing even happens with the two seasons - season one of Hamatora is great but the second season gets darker faster and the plot line is pretty intricate and fun to follow. 10/10 would recommend if you liked Bungo :)
Let's leave the goofy ol.. sitcom... and move to the character.. developments..
Since the first season is full of whacky moments unless when the sequel is just about to get serious than before...
Familiar about "SHITS ABOUT TO GET REAL..." and 0-100% REAL QUICK scene..
Both shows have a tight knit family of friends who have to fight to survive as part of an agency of sorts. Both shows have esper and supernatural elements and have a perfect mix of darkness, sarcasm, and lighter humor.
Both shows are relatively short, but have interesting stories that are occasionally shrouded in mystery, and both shows focus on character development by way of flashbacks and history.
The second season of Bungo, which is fairly highly regarded, actually reminded me a lot of The Unlimited, which came out a few years before, but is criminally under rated and largely forgotten.
If you liked Bungo, but wished it was less of a Shounen fighter and more story based, then The Unlimited is for you.  read more
Charlotte and Bungou Stray Dogs (BSD) 2nd Season are both about people with supernatural abilities trying to find justice. Although both have comic relief, they both weave in darker elements involving the main characters' backgrounds. Also the main characters of Charlotte share a bit of Dazai's OP-ness. However, Charlotte has quite a bit of romance, unlike BSD, but overall I put them both in high regard.
Well, you may look at it this way:
-They both have GUILDS!
-both have the evil groups and good ones
-they both have comedy (although Fairy Tail has waaay more)
The only difference is that Stray Dogs has more of a story that develops rather than in Fairy Tail where they do have a story but it's not fully developed like SD. It's confusing but once you watch both, you'll see what I mean)
both about agencies that work to make the world a better place. both have fairly dense and self pitying main characters; who are orphans; that have mentors that work to make them better people, in spite of their own questionable past.
These series feature an atmosphere of somewhat mature darkness that centers around a mystery theme. Most of the main characters are male, and the aesthetic style is very similar. If you appreciated the style of Bungou Stray Dogs and wished it took the mystery theme further, give Mouryou no Hako a try.
However, Bungou Stray Dogs is considerably more action-oriented and Mouryou no Hako is more dialogue-centric with horror elements.