I am writing this as a comparison between BSD and BTA.
Bungo stray dogs (BSD) is a quite famous anime show, and its characters are inspired by Japanese historical writers and their works.Bungo Stray Dogs is the story about mafia, dectectives, criminals mixed with a twist of supernatural abilities.
Bungo to Alchemist (BTA), which released only this spring, is also an anime show which has characters that are inspired by the Japanese historical writers like Osamu Dazai, Ryunosuke Akutagawa, Nakahara Chuuya and many many more.Bungo to Alchemist is a show about reincarnated writers who delve into books to protect them from Taints, which is an evil force that manipulates the world inside the book and destroys it.
Bungo Stray Dogs is set in a world teeming with individuals with supernatural abilities, whose characters are named and inspired by japanese famous writes like Osamu Dazai, Atsushi Nakajima, Sakaguchi Ango, Kunikida Doppo etc. and their supernatural abilities are named after the most famous works of the author (now you know why the names of their abilities were so typical and that their abilities derived from their names and it was not the other way round!), like, Osamu Dazai's ability 'No Longer Human' is a famous work of the real author Osamu Dazai and also Dazai's suicidal nature and his dream to commit a double suicide with a beautiful women and also the fact that he kept failing at them was actually inspired by his real world counterpart. Akutagawa Ryunosuke's ability 'Rashomon' is a famous work of the real author Akutagawa Ryunosuke. But BSD as a show is nowhere around authors, and only the characters are inspired and not the story.
Bungo to Alchemist, is set up in a world where the old literatures have started disappearing and the authors have been reincarnated to protect them from the taints. Now, this is a show which is actually very much inspired by the real world authors, and actually revolves around these authors and their works. Showing many of their praised works, stating it's phrases and letting the audience know what kind of a person they were in real life, not an autobiography but basically makes you aware about classic Japanese literature and is more realistic about the lives of the different authors.
"I watched BSD, shall I watch BTA too"?
In my opinion, No, It's not necessary that if you watched BSD and liked it, you need to watch BTA, they both are totally different, you might get attracted by the fact that they have characters with same name but it's not necessay that if you liked BSD, you are going to like BTA too, since they both come from different genre. BTA revolves around the fact that the world would not be the same place if all the literature work ceased to exist, but it's not the case with BSD.
"Do I need to have the knowledge of Japanese literature, before watching BSD/BTA?
To watch BSD, you don't need to have knowledge about Japanese literature, because BSD nowhere deals with their work of literature and has a totally unique storyline. To watch BTA, I would say, Yes, or so I feel that you need have a little knowledge of Japanese literature, because otherwise you will find yourself dumbfounded because even though you know some characters and their traits, because you watched BSD; BTA is actually a lot more, it takes you more deep about the works of literature and the authors themselves.
What is different or same about characters of BSD/BTA?
Well, the names of some characters and also some of their traits are same because they are actually inspired by the real world counterpart, like, Dazai's suicidal nature; Ango, Odasuke and Dazai being bestfriends; Kenji being a simpleton; Nakahara Chuuya is found of fancy hats. But there are many who are different, like Akutagawa Ryunosuke, was a complicated character in BSD who barely got any respect from Dazai, which he longed for; but the Akutagawa of BTA is totally different, he is actually the most mature and intelligent of them all and Dazai actually respects him like his teacher, also all the others like Chuuya, Ango and Odasuke respects him more than anybody else. There are many other characters who I don't think have ever made an appearance in BSD like Hagiwara Sakutarou, Shimazaki Touson, Tokuda Shuusei and many other that will make their appearance later on in BTA, so BTA is totally about authors, literature and why we cannot let these works of art disappear from the society.
This I have written from my personal experience since I like both the shows, If you would like to make changes about any fact or add up any question, feel free to tell me in my comments!